Question

For my exams please no wrong answers
Using the Venn diagram find the following sets.
(i) A' ∪ B' (ii) A' ∩ B' (iii) A – ( B ∪ C ) (iv) A – ( B ∩ C )

20 points

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

(i) ⇒ (ii)

We know that, A−B={x∈A:x



∈B}

Since A⊂B. Therefore, there is no element in A which does not belong to B.

∴A−B=ϕ

Hence, (i) ⇒ (ii).

(ii) ⇒ (ii)

We have, A−B=ϕ⇒A⊂B⇒A∪B=B

Hence, (ii) ⇒ (iii).

(iii) ⇒ (iv)

We have, A∪B=B⇒A⊂B⇒A∩B=A

Hence, (iii) ⇒ (iv).

(iv) ⇒ (ii)

We have, A∩B=A⇒A⊂B

Hence, (iv)⇒ (ii)

Consequently, (ii) ⇔ (ii) ⇔ (iii) ⇔ (iv)

Answer 2

Answer:

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Step-by-step:-

(i) ⇒ (ii)

We know that, A−B={x∈A:x



∈B}

Since A⊂B. Therefore, there is no element in A which does not belong to B.

∴A−B=ϕ

Hence, (i) ⇒ (ii).

(ii) ⇒ (ii)

We have, A−B=ϕ⇒A⊂B⇒A∪B=B

Hence, (ii) ⇒ (iii).

(iii) ⇒ (iv)

We have, A∪B=B⇒A⊂B⇒A∩B=A

Hence, (iii) ⇒ (iv).

(iv) ⇒ (ii)

We have, A∩B=A⇒A⊂B

Hence, (iv)⇒ (ii)

Consequently, (ii) ⇔ (ii) ⇔ (iii) ⇔ (iv)