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Let p, q, r, s represents the following propositions.
p: x ∈ {8, 9, 10, 11, 12}
q: x is a composite number
r: x is a perfect square
s: x is a prime number
The integer x ≥ 2 which satisfies ¬ ((p ⇒ q) ∧ (¬ r ∨ ¬ s)) is __________ 
    Correct answer is '11'. Can you explain this answer?
    Most Upvoted Answer
    Let p, q, r, s represents the following propositions.p: x ∈ {8, 9...
    Data:
    p: x ∈ {8, 9, 10, 11, 12}
    q: x is a composite number
    r: x is a perfect square
    s: x is a prime number
    Explanation:
    p ⇒ q means p̅ + q
    As, q is composite number So, p ⇒ results in {8, 9, 10, 12}
    As, r: x is a perfect square, ¬ r results in all the numbers which are not perfect square
    So, ¬ r: {8, 10, 11, 12}
    ¬ s: {8, 9, 10, 12}
    ¬ r ∨ ¬ s = {8, 9, 10, 11, 12}
    Now, (p ⇒ q) ∧ (¬ r ∨ ¬ s) = {8, 9, 10, 12}
    ¬ ((p ⇒ q) ∧ (¬ r ∨ ¬ s)) results in a number which is not present in ((p ⇒ q) ∧ (¬ r ∨ ¬ s))
    ¬ ((p ⇒ q) ∧ (¬ r ∨ ¬s)) will give {11}.
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    Let p, q, r, s represents the following propositions.p: x ∈ {8, 9, 10, 11, 12}q: x is a composite numberr: x is a perfect squares: x is a prime numberThe integer x ≥ 2 which satisfies ¬ ((p ⇒ q) ∧ (¬ r ∨ ¬ s)) is __________Correct answer is '11'. Can you explain this answer?
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