Question

for non empty sets A and B then (AUB) whole compliment =?​

Answer 1

Answer:

• is just a simple application of DeMorgan's complement law which states that for any two sets A, B ;. (I) (AUB)' = (A' n B') and. (II) (AnB)' .
• If A and B are non empty sets, then ( A-B)uu(B-A) equals. Updated On: 27-7-2020. 598.9 K. like. 247.0 K. dislike. 1x 1.5x 2x.

It indicates B is a empty set or have same elements which set A have because at union fuction also the answer is A.

Step-by-step explanation:

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Answer 2

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Let M = (A ∩ B)' and N = A' U B'

Let x be an arbitrary element of M then x ∈ M ⇒ x ∈ (A ∩ B)'

⇒ x ∉ (A ∩ B)

⇒ x ∉ A or x ∉ B

⇒ x ∈ A' or x ∈ B'

⇒ x ∈ A' U B'

⇒ x ∈ N

Therefore, M ⊂ N …………….. (i)

Again, let y be an arbitrary element of N then y ∈ N ⇒ y ∈ A' U B'

⇒ y ∈ A' or y ∈ B'

⇒ y ∉ A or y ∉ B

⇒ y ∉ (A ∩ B)

⇒ y ∈ (A ∩ B)'

⇒ y ∈ M

Therefore, N ⊂ M …………….. (ii)

Now combine (i) and (ii) we get; M = N i.e. (A ∩ B)' = A' U B'

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