Question

show that (A')'=A how can we prove this Question

Answer 1

Step-by-step explanation:

Let an universal set € that contains english alphabet.

So,

€ = { a, b, c, d,... z }

Let A be any set of vowels,

A = { a, e, i, o, u }

• A' refers to the set of elements which are a part of universal set but not of A.

Here, the letters except vowels are consonants, that's how

A' = { b, c, d,... z }

But, similarly, (A')' refers to the set of elements which are a part of universal set but not of A'( consonants).

So, (A')' must have vowels only. Therefore,

(A')' = { a, e, i, o, u }

From above, we see, { a, e, i, o, u } = A

Hence,

(A')' = { a, e, i, o, u } = A

(A')' = A

Proved.