Question

let P be the set of primenummbers and let S=t. s subset of P

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Answer 1

Answer:

Now the equivalent contrapositive statement of x ∈ S ⇒ x ∈ P is x ∉ P ⇒ x ∉ S.

Now, we will prove the above contrapositive statement by contradiction method Let x ∉ P ⇒ x is a composite number

Let us now assume that x ∈ S ⇒

2x – 1 = m (where m is a prime number)

⇒ 2x = m + 1

Which is not true for all composite number, say for x = 4 because 24 = 16 which can not be equal to the sum of any prime number m and 1.

Thus, we arrive at a contradiction

⇒ x ∉ S. Thus, when x ∉ P, we arrive at x ∉ S

So, S ⊂ p.

Explanation:

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