MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If x * y = x + y + xy then (G, *) is _____________ |
| A. | Monoid |
| B. | Abelian group |
| C. | Commutative semigroup |
| D. | Cyclic group |
| Answer» D. Cyclic group | |
| 2. |
A function defined by f(x)=2*x such that f(x+y)=2x+y under the group of real numbers, then ________ |
| A. | Isomorphism exists |
| B. | Homomorphism exists |
| C. | Heteromorphic exists |
| D. | Association exists |
| Answer» C. Heteromorphic exists | |
| 3. |
A function f:(M,∗)→(N,×) is a homomorphism if ______a) f(a, b) = a*bb) f(a, b) = a/bc) f(a, b) = f(a)+f(b)d) f(a, b) = f(a)*f( |
| A. | f(a, b) = a*bb) f(a, b) = a/bc) f(a, b) = f(a)+f(b)d) f(a, |
| B. | = a*bb) f(a, b) = a/b |
| C. | f(a, b) = f(a)+f(b) |
| D. | f(a, b) = f(a)*f(a) |
| Answer» C. f(a, b) = f(a)+f(b) | |
| 4. |
Condition of semigroup homomorphism should be ____________ |
| A. | f(x * x) = f(x * y) |
| B. | f(x) = f(y) |
| C. | f(x) * f(y) = f(y) |
| D. | f(x * y) = f(x) * f(y) |
| Answer» E. | |
| 5. |
The set of rational numbers form an abelian group under _________ |
| A. | Association |
| B. | Closure |
| C. | Multiplication |
| D. | Addition |
| Answer» D. Addition | |
| 6. |
If F is a free semigroup on a set S, then the concatenation of two even words is ________ |
| A. | a semigroup of F |
| B. | a subgroup of F |
| C. | monoid of F |
| D. | cyclic group of F |
| Answer» C. monoid of F | |
| 7. |
The set of odd and even positive integers closed under multiplication is ________ |
| A. | a free semigroup of (M, ×) |
| B. | a subsemigroup of (M, ×) |
| C. | a semigroup of (M, ×) |
| D. | a subgroup of (M, ×) |
| Answer» C. a semigroup of (M, ×) | |
| 8. |
If a * b = a such that a ∗ (b ∗ c) = a ∗ b = a and (a * b) * c = a * b = a then ________ |
| A. | * is associative |
| B. | * c = a * b = a then ________a) * is associativeb) * is commutative |
| C. | = a ∗ b = a and (a * b) * c = a * b = a then ________a) * is associativeb) * is commutativec) * is closure |
| D. | * is abelian |
| Answer» B. * c = a * b = a then ________a) * is associativeb) * is commutative | |
| 9. |
A subgroup has the properties of ________ |
| A. | Closure, associative |
| B. | Commutative, associative, closure |
| C. | Inverse, identity, associative |
| D. | Closure, associative, Identity, Inverse |
| Answer» E. | |
| 10. |
__________ are called group postulates. |
| A. | Group lemmas |
| B. | Group theories |
| C. | Group axioms |
| D. | Group |
| Answer» D. Group | |