True

According to the question,

There are three sets A, B and C

To check: if A ⊂ B, then A ∩ C ⊂ B ∩ C is true or false

Let x ∈ A ∩ C

⇒ x ∈ A and x ∈ C

⇒ x ∈ B and x ∈ C {∵ A ⊂ B}

⇒ x ∈ B ∩ C

⇒ A ∩ C ⊂ B ∩ C

Hence, the given statement “for all sets A, B and C, if A ⊂ B, then A ∩ C ⊂ B ∩ C” is true.

True

According to the question,

There are three sets A, B and C

To check: if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C is true or false

Let x ∈ A ∪ B

⇒ x ∈ A or x ∈ C

⇒ x ∈ C or x ∈ C {∵ A ⊂ C and B ⊂ C}

⇒ x ∈ C

⇒ A ∪ B ⊂ C

Hence, the given statement “for all sets A, B and C, if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C” is true

True

According to the question,

There are three sets A, B and C

To check: if A ⊂ B, then A ∪ C ⊂ B ∪ C is true or false

Let x ∈ A ∪ C

⇒ x ∈ A or x ∈ C

⇒ x ∈ B or x ∈ C {∵ A ⊂ B}

⇒ x ∈ B ∪ C

⇒ A ∪ C ⊂ B ∪ C

Hence, the given statement “for all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C” is true

True

According to the question,

There are two sets A and B

To check: (A – B) ∪ (A ∩ B) = A is true or false

L.H.S = (A – B) ∪ (A ∩ B)

Since, A – B = A ∩ B’,

We get,

= (A ∩ B’) ∪ (A ∩ B)

Using distributive property of set:

We get,

(A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)

= A ∩ (B’ ∪ B)

= A ∩ U

= A

= R.H.S

Hence, the given statement “for all sets A and B, (A – B) ∪ (A ∩ B) = A” is true