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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 851. |
If matrix \[A=\left[ \begin{matrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{matrix} \right]\] then find\[tr(A)+tr({{A}^{2}})+tr({{A}^{3}})+...+tr({{A}^{100}})\] |
| A. | 100 |
| B. | 50 |
| C. | 200 |
| D. | None of these |
| Answer» D. None of these | |
| 852. |
If \[A=\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] then \[{{A}^{100}}\]: |
| A. | \[{{2}^{100}}A\] |
| B. | \[{{2}^{99}}A\] |
| C. | \[{{2}^{101}}A\] |
| D. | None of above |
| Answer» C. \[{{2}^{101}}A\] | |
| 853. |
If \[A=\left( \begin{matrix} p & q \\ 0 & 1 \\ \end{matrix} \right)\], then \[{{A}^{8}}=\left( \begin{matrix} {{p}^{8}} & q\left( \frac{{{p}^{8}}-1}{p-1} \right) \\ 0 & k \\ \end{matrix} \right)\]. The value of k is |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | -1 |
| Answer» B. 0 | |
| 854. |
If \[P\left[ \begin{matrix} \cos (\pi /6) & \sin (\pi /6) \\ -\sin (\pi /6) & \cos (\pi /6) \\ \end{matrix} \right],A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\] and \[Q=PAP'\] then \[P'{{Q}^{2007}}P\] is equal to |
| A. | \[\left[ \begin{matrix} 1 & 2007 \\ 0 & 1 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 1 & \sqrt{3}/2 \\ 0 & 2007 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} \sqrt{3}/2 & 2007 \\ 0 & 1 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} \sqrt{3}/2 & -1/2 \\ 1 & 2007 \\ \end{matrix} \right]\] |
| Answer» B. \[\left[ \begin{matrix} 1 & \sqrt{3}/2 \\ 0 & 2007 \\ \end{matrix} \right]\] | |
| 855. |
If \[A=\left[ \begin{matrix} 1 & 2 \\ 0 & 3 \\ \end{matrix} \right]\] is a \[2\times 2\] matrix and \[f(x)={{x}^{2}}-x+2\] is a polynomial, then what is f(A)? |
| A. | \[\left[ \begin{matrix} 1 & 7 \\ 1 & 7 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 2 & 6 \\ 0 & 8 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 2 & 6 \\ 0 & 6 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} 2 & 6 \\ 0 & 7 \\ \end{matrix} \right]\] |
| Answer» C. \[\left[ \begin{matrix} 2 & 6 \\ 0 & 6 \\ \end{matrix} \right]\] | |
| 856. |
The matrix \[A=\left[ \begin{matrix} 1 & 3 & 2 \\ 1 & x-1 & 1 \\ 2 & 7 & x-3 \\ \end{matrix} \right]\] will have inverse for every real number x except for |
| A. | \[x=\frac{11\pm \sqrt{5}}{2}\] |
| B. | \[x=\frac{9\pm \sqrt{5}}{2}\] |
| C. | \[x=\frac{11\pm \sqrt{3}}{2}\] |
| D. | \[x=\frac{9\pm \sqrt{3}}{2}\] |
| Answer» B. \[x=\frac{9\pm \sqrt{5}}{2}\] | |
| 857. |
If \[A=\left[ \begin{matrix} 2 & 2 \\ 2 & 2 \\ \end{matrix} \right]\], then what is \[{{A}^{n}}\] equal to? |
| A. | \[\left[ \begin{matrix} {{2}^{n}} & {{2}^{n}} \\ {{2}^{n}} & {{2}^{n}} \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 2n & 2n \\ 2n & 2n \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} {{2}^{2n-1}} & {{2}^{2n-1}} \\ {{2}^{2n-1}} & {{2}^{2n-1}} \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} {{2}^{2n+1}} & {{2}^{2n+1}} \\ {{2}^{2n+1}} & {{2}^{2n+1}} \\ \end{matrix} \right]\] |
| Answer» D. \[\left[ \begin{matrix} {{2}^{2n+1}} & {{2}^{2n+1}} \\ {{2}^{2n+1}} & {{2}^{2n+1}} \\ \end{matrix} \right]\] | |
| 858. |
If AB = O, then for the matrices \[A=\left[ \begin{matrix} {{\cos }^{2}}\theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & {{\sin }^{2}}\theta \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} {{\cos }^{2}}\phi & \cos \phi \sin \phi \\ \cos \phi \sin \phi & {{\sin }^{2}}\phi \\ \end{matrix} \right],\theta -\phi \] is |
| A. | An odd number of \[\frac{\pi }{2}\] |
| B. | An odd multiple of \[\pi \] |
| C. | An even multiple of \[\frac{\pi }{2}\] |
| D. | 0 |
| Answer» B. An odd multiple of \[\pi \] | |
| 859. |
The element \[{{a}_{ij}}\] of square matrix is given by \[{{a}_{ij}}=(i+j)(i-j)\], then matrix A must be |
| A. | Skew-symmetric matrix |
| B. | Triangular matrix |
| C. | Symmetric matrix |
| D. | Null matrix |
| Answer» B. Triangular matrix | |
| 860. |
Let \[A=\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right]\] be a square matrix of order 3. Then for any positive integer n, what is \[{{A}^{n}}\] equal to? |
| A. | A |
| B. | \[{{3}^{n}}A\] |
| C. | \[({{3}^{n-1}})A\] |
| D. | 3A |
| Answer» D. 3A | |
| 861. |
If A is a square matrix such that \[(A-2I)(A+I)=O\]then \[{{A}^{-1}}=\] |
| A. | \[\frac{A-I}{2}\] |
| B. | \[\frac{A+I}{2}\] |
| C. | \[2(A-I)\] |
| D. | \[2A+I\] |
| Answer» B. \[\frac{A+I}{2}\] | |
| 862. |
Number of square sub-matrices of order 2 (sub-matrix is obtained by deleting appropriate number of rows and columns in a given matrix) that can be formed from the matrix \[\left[ \begin{matrix} 1 & 2 & -1 & 4 \\ 2 & 4 & 3 & 5 \\ -1 & -2 & 6 & -7 \\ \end{matrix} \right]\] is |
| A. | 12 |
| B. | 15 |
| C. | 18 |
| D. | \[{{2}^{12}}\] |
| Answer» D. \[{{2}^{12}}\] | |
| 863. |
If \[A=\left[ \begin{matrix} 1 & 0 \\ -1 & 7 \\ \end{matrix} \right]\] and \[I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\], then the value of k so that \[{{A}^{2}}=8A+kI\] is |
| A. | \[k=7\] |
| B. | \[k=-7\] |
| C. | \[k=0\] |
| D. | None of these |
| Answer» C. \[k=0\] | |
| 864. |
Let \[A=\left[ \begin{align} & \begin{matrix} 5 & 6 & 1 \\ \end{matrix} \\ & \begin{matrix} 2 & -1 & 5 \\ \end{matrix} \\ \end{align} \right]\]. Let there exist a matrix B such that \[AB=\left[ \begin{matrix} 35 & 49 \\ 29 & 13 \\ \end{matrix} \right]\]. What is B equal to? |
| A. | \[\left[ \begin{align} & \begin{matrix} 5 & 1 & 4 \\ \end{matrix} \\ & \begin{matrix} 2 & 6 & 3 \\ \end{matrix} \\ \end{align} \right]\] |
| B. | \[\left[ \begin{align} & \begin{matrix} 2 & 6 & 3 \\ \end{matrix} \\ & \begin{matrix} 5 & 1 & 4 \\ \end{matrix} \\ \end{align} \right]\] |
| C. | \[\left[ \begin{align} & \begin{matrix} 5 & 2 \\ \end{matrix} \\ & \begin{matrix} 1 & 6 \\ \end{matrix} \\ & \begin{matrix} 4 & 3 \\ \end{matrix} \\ \end{align} \right]\] |
| D. | \[\left[ \begin{align} & \begin{matrix} 2 & 5 \\ \end{matrix} \\ & \begin{matrix} 6 & 1 \\ \end{matrix} \\ & \begin{matrix} 3 & 4 \\ \end{matrix} \\ \end{align} \right]\] |
| Answer» D. \[\left[ \begin{align} & \begin{matrix} 2 & 5 \\ \end{matrix} \\ & \begin{matrix} 6 & 1 \\ \end{matrix} \\ & \begin{matrix} 3 & 4 \\ \end{matrix} \\ \end{align} \right]\] | |
| 865. |
If A is any \[2\times 2\] matrix such that \[\left[ \begin{matrix} 1 & 2 \\ 0 & 3 \\ \end{matrix} \right]A=\left[ \begin{matrix} -1 & 0 \\ 6 & 3 \\ \end{matrix} \right]\], then what is A equal to? |
| A. | \[\left[ \begin{matrix} -5 & 1 \\ -2 & 2 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} -5 & -2 \\ 1 & 2 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} -5 & -2 \\ 2 & 1 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} 5 & 2 \\ -2 & -1 \\ \end{matrix} \right]\] |
| Answer» D. \[\left[ \begin{matrix} 5 & 2 \\ -2 & -1 \\ \end{matrix} \right]\] | |
| 866. |
If \[A={{[{{a}_{ij}}]}_{n\times n}}\] be a diagonal matrix with diagonal element all different and \[B={{[{{b}_{ij}}]}_{n\times n}}\] be some another matrix. Let \[AB={{[cij]}_{n\times n}}\]then \[{{c}_{ij}}\] is equal to |
| A. | \[{{a}_{jj}}{{b}_{ij}}\] |
| B. | \[{{a}_{ii}}\,{{b}_{ij}}\] |
| C. | \[{{a}_{ij}}\,{{b}_{ij}}\] |
| D. | \[{{a}_{ij}}\,{{b}_{ji}}\] |
| Answer» C. \[{{a}_{ij}}\,{{b}_{ij}}\] | |
| 867. |
Consider the matrices \[A=\left[ \begin{matrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \\ \end{matrix} \right],B=\left[ \begin{align} & \begin{matrix} 2 & 4 \\ \end{matrix} \\ & \begin{matrix} 0 & 1 \\ \end{matrix} \\ & \begin{matrix} -1 & 2 \\ \end{matrix} \\ \end{align} \right],C=\left[ \begin{matrix} 3 \\ 1 \\ 2 \\ \end{matrix} \right]\] Out of the given matrix products, which one is not defined. |
| A. | \[{{(AB)}^{T}}C\] |
| B. | \[{{C}^{T}}C{{(AB)}^{T}}\] |
| C. | \[{{C}^{T}}AB\] |
| D. | \[{{A}^{T}}AB{{B}^{T}}C\] |
| Answer» C. \[{{C}^{T}}AB\] | |
| 868. |
If \[A=\left[ \begin{matrix} 0 & 1 & 3 \\ 1 & 2 & 3 \\ 3 & a & 1 \\ \end{matrix} \right]\] and \[{{A}^{-1}}=\left[ \begin{matrix} 1/2 & -1/2 & 1/2 \\ -4 & 3 & c \\ 5/2 & -3/2 & 1/2 \\ \end{matrix} \right]\] Then the value of \[a+c\]is equal to |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | None of these |
| Answer» C. 2 | |
| 869. |
Matrix A such that \[{{A}^{2}}=2A-I\], where I is the identity matrix, then for \[n\ge 2,\text{ }{{\text{A}}^{n}}\] is equal to |
| A. | \[{{2}^{n-1}}A-(n-1)I\] |
| B. | \[{{2}^{n-1}}A-I\] |
| C. | \[nA-(n-1)I\] |
| D. | \[nA-I\] |
| Answer» D. \[nA-I\] | |
| 870. |
If A and B be two square matrices of order \[\lambda \]whose all the elements are essentially positive integers then the minimum value of \[tr\text{ (}A{{B}^{2}})\] is equal to |
| A. | \[{{\lambda }^{3}}\] |
| B. | \[{{\lambda }^{2}}\] |
| C. | \[2{{\lambda }^{2}}\] |
| D. | None of these |
| Answer» C. \[2{{\lambda }^{2}}\] | |
| 871. |
Let \[A=\left[ \begin{matrix} x+y & y \\ 2x & x-y \\ \end{matrix} \right],B=\left[ \begin{matrix} 2 \\ -1 \\ \end{matrix} \right]\] and \[C=\left[ \begin{matrix} 3 \\ 2 \\ \end{matrix} \right]\] If \[AB=C,\] then what is \[{{A}^{2}}\] equal to? |
| A. | \[\left[ \begin{matrix} 6 & -10 \\ 4 & 26 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} -10 & 5 \\ 4 & 24 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} -5 & -6 \\ -4 & -20 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} -5 & -7 \\ -5 & 20 \\ \end{matrix} \right]\] |
| Answer» B. \[\left[ \begin{matrix} -10 & 5 \\ 4 & 24 \\ \end{matrix} \right]\] | |
| 872. |
If \[A=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\], then \[{{A}^{16}}\] is equal to: |
| A. | \[\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} -1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] |
| Answer» E. | |
| 873. |
Elements of a matrix A of order \[10\times 10\] are defined as \[{{a}_{ij}}={{w}^{i+j}}\] (where w is cube root of unity), then trof the matrix is |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | None of these |
| Answer» E. | |
| 874. |
sLet \[A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} a & 0 \\ 0 & b \\ \end{matrix} \right]\] where a, b are natural numbers, then which one of the following is correct? |
| A. | There exist more than one but finite number of B's such that AB = BA |
| B. | There exists exactly one B such that AB = BA |
| C. | There exist infinitely many B's such that AB=BA |
| D. | There cannot exist any B such that AB = BA |
| Answer» D. There cannot exist any B such that AB = BA | |
| 875. |
If number of elements is 20 then how many different types of matrices can be formed if number of rows is always even? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» C. 5 | |
| 876. |
The matrix \[A=\left[ \begin{matrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{matrix} \right]\] is |
| A. | Idempotent matrix |
| B. | Involutory matrix |
| C. | Nilpotent matrix |
| D. | None of these |
| Answer» C. Nilpotent matrix | |
| 877. |
Which of the following is not a statement? |
| A. | Please do me a favour |
| B. | 2 is an even integer |
| C. | \[2+1=3\] |
| D. | The number 17 is prime |
| Answer» B. 2 is an even integer | |
| 878. |
If p and q are two statement then \[(p\leftrightarrow \tilde{\ }q)\] is true when- |
| A. | p and q both are true |
| B. | p and q both are false |
| C. | p is false and q is true |
| D. | None of these |
| Answer» D. None of these | |
| 879. |
The false statement of the following is |
| A. | \[p\wedge (\tilde{\ }p)\] is a contradiction |
| B. | \[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \tilde{\ }p)\] is a contradiction |
| C. | \[\tilde{\ }(\tilde{\ }p)\Leftrightarrow p\] is a tautology |
| D. | \[p\vee (\tilde{\ }p)\Leftrightarrow p\] is a tautology |
| Answer» C. \[\tilde{\ }(\tilde{\ }p)\Leftrightarrow p\] is a tautology | |
| 880. |
If p is nay statement, then which of the following is a tautology? |
| A. | \[p\wedge f\] |
| B. | \[p\vee f\] |
| C. | \[p\vee (\tilde{\ }p)\] |
| D. | \[p\wedge t\] |
| Answer» D. \[p\wedge t\] | |
| 881. |
\[\tilde{\ }(p\Rightarrow q)\Leftrightarrow \tilde{\ }p\vee \tilde{\ }q\] is |
| A. | A tautology |
| B. | A contradiction |
| C. | Neither a tautology nor a contradiction |
| D. | Cannot come to any conclusion |
| Answer» D. Cannot come to any conclusion | |
| 882. |
The contrapositive of the statement, ?If I do not secure good marks then I cannot go for engineering?, is |
| A. | If I secure good marks, then I go for engineering |
| B. | If I go for engineering then I secure good marks |
| C. | If I cannot go for engineering then I do not secure good marks |
| D. | None |
| Answer» C. If I cannot go for engineering then I do not secure good marks | |
| 883. |
Let p be the proposition: Mathematics is a interesting and let q be the propositions that Mathematics is difficult, then the symbol \[p\wedge q\]means |
| A. | Mathematics is interesting ipllies that Mathematics is difficult |
| B. | Mathematics is interesting impels and is implied by Mathematics is difficult |
| C. | Mathematics is interesting and Mathematics is difficult |
| D. | Mathematics is interesting or Mathematics is difficult |
| Answer» D. Mathematics is interesting or Mathematics is difficult | |
| 884. |
Which of the following is a contradiction? |
| A. | \[(p\wedge q)\wedge \tilde{\ }(p\vee q)\] |
| B. | \[p\vee (-p\wedge q)\] |
| C. | \[(p\Rightarrow q)\Rightarrow p\] |
| D. | None of these |
| Answer» B. \[p\vee (-p\wedge q)\] | |
| 885. |
If p: 4 is an even prime number, q: 6 is a divisor of 12 and r: the HCF of 4 and 6 is 2, then which one of the following is true? |
| A. | \[(p\wedge q)\] |
| B. | \[(p\vee q)\wedge \tilde{\ }r\] |
| C. | \[\tilde{\ }(q\wedge r)p\] |
| D. | \[\tilde{\ }p\vee (q\wedge r)\] |
| Answer» E. | |
| 886. |
In the truth table for the statement \[(p\to q)\leftrightarrow (\tilde{\ }p\vee q),\] the last column has the truth value in the following order is |
| A. | \[TTFF\] |
| B. | \[FFFF\] |
| C. | \[TTTT\] |
| D. | \[FTFT\] |
| Answer» D. \[FTFT\] | |
| 887. |
The contrapositive of the inverse of \[p\Rightarrow \tilde{\ }q\] is |
| A. | \[\tilde{\ }q\Rightarrow p\] |
| B. | \[p\Rightarrow q\] |
| C. | \[\tilde{\ }q\Rightarrow \tilde{\ }p\] |
| D. | \[\tilde{\ }p\Rightarrow \tilde{\ }q\] |
| Answer» B. \[p\Rightarrow q\] | |
| 888. |
The negation of the statement ?A circle is an ellipse?? is |
| A. | An ellipse is a circle |
| B. | An ellipse is not a circle |
| C. | A circle is not an ellipse |
| D. | A circle is an ellipse |
| Answer» D. A circle is an ellipse | |
| 889. |
Which of the following is not logically equivalent to the proposition: 'A real number is either rational or irrational.'? |
| A. | If a number is neither rational n nor irrational then it is not real |
| B. | If a number is not a rational or not an irrational, then it is not real |
| C. | If a number is not real, then it is neither rational nor irrational |
| D. | If a number is real, then it is rational or irrational. |
| Answer» C. If a number is not real, then it is neither rational nor irrational | |
| 890. |
The propositions \[(p\Rightarrow \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a |
| A. | Tautology and contradiction |
| B. | Neither tautology nor contradiction |
| C. | Contradiction |
| D. | Tautology |
| Answer» D. Tautology | |
| 891. |
The negation of the statement \[(p\wedge q)\to (\tilde{\ }p\vee r)\]is |
| A. | \[(p\wedge q)\vee (p\vee \tilde{\ }r)\] |
| B. | \[(p\wedge q)\vee (p\wedge \tilde{\ }r)\] |
| C. | \[(p\wedge q)\wedge (p\wedge \tilde{\ }r)\] |
| D. | \[p\vee q\] |
| Answer» D. \[p\vee q\] | |
| 892. |
If p: Ashok works hard q: Ashok gets good grade The verbal form for \[(\tilde{\ }p\to q)\] is |
| A. | If Ashok works hard then gets good grade |
| B. | If Ashok does not work hard then he gets good grade |
| C. | If Ashok does not work hard then he does not get good grade |
| D. | Ashok works hard if and only if he gets grade |
| Answer» C. If Ashok does not work hard then he does not get good grade | |
| 893. |
If \[p\Rightarrow (q\vee r)\] is false, then the truth values of \[p,q,r\] are respectively |
| A. | \[T,F,F\] |
| B. | \[F,F,F\] |
| C. | \[F,T,T\] |
| D. | \[T,T,F\] |
| Answer» B. \[F,F,F\] | |
| 894. |
Negation of the conditional: 'If it rains, I shall go to school'? is |
| A. | It rains and I shall go to school |
| B. | It runs and I shall not go to school |
| C. | It does not rains and I shall go to school |
| D. | None of these |
| Answer» C. It does not rains and I shall go to school | |
| 895. |
If :p Raju is tall and q: Raju is intelligent, then the symbolic statement \[\tilde{\ }p\vee q\] means |
| A. | Raju is not tall or he is intelligent. |
| B. | Raju is tall or he is intelligent |
| C. | Raju is not tall and he is intelligent |
| D. | Raju is not tall implies he is intelligent |
| Answer» B. Raju is tall or he is intelligent | |
| 896. |
Let p and q be any two logical statements and \[r:p\to (\tilde{\ }p\vee q).\] If r has a truth value F, then the truth values of p and q are respectively: |
| A. | F, F |
| B. | T, T |
| C. | T, F |
| D. | F, T |
| Answer» D. F, T | |
| 897. |
Identify the false statements |
| A. | \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\vee q\] |
| B. | \[[p\vee q]\vee (\tilde{\ }p)\] is a tautology |
| C. | \[[p\wedge q)\wedge (\tilde{\ }p)\] is a contradiction |
| D. | \[\tilde{\ }[p\vee q]\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\] |
| Answer» E. | |
| 898. |
The inverse of the statement \[(p\wedge \tilde{\ }q)\to r\] is |
| A. | \[\tilde{\ }(p\vee \tilde{\ }q)\to \tilde{\ }r\] |
| B. | \[(\tilde{\ }p\wedge q)\to \tilde{\ }r\] |
| C. | \[(\tilde{\ }p\vee q)\to \tilde{\ }r\] |
| D. | None of these |
| Answer» D. None of these | |
| 899. |
The statement \[p\to (q\to p)\]is equivalent to |
| A. | \[p\to (p\to q)\] |
| B. | \[p\to (p\vee q)\] |
| C. | \[p\to (p\wedge q)\] |
| D. | \[p\to (p\leftrightarrow q)\] |
| Answer» E. | |
| 900. |
Which of the following is always true? |
| A. | \[(\tilde{\ }p\vee \tilde{\ }q)\equiv (p\wedge q)\] |
| B. | \[(p\to q)\equiv (\tilde{\ }q\to \tilde{\ }p)\] |
| C. | \[\tilde{\ }(p\to \tilde{\ }q)\equiv (p\wedge \tilde{\ }q)\] |
| D. | \[\tilde{\ }(p\leftrightarrow q)\equiv (p\to q)\to (q\to p)\] |
| Answer» C. \[\tilde{\ }(p\to \tilde{\ }q)\equiv (p\wedge \tilde{\ }q)\] | |