Consider universe positive integer X= {1 ≤ n ≤ 8}, proposition P= "n is an even integers", Q = "(3 ≤ n ≤ 7) ^ (n ≠ 6)". Then truth set of P ↔ Q is 

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UGC NET Computer Science (Paper 2) 17 June 2023 Official Paper
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  1. {1, 4}
  2. {2, 6}
  3. {3, 4, 5}
  4. {1}

Answer (Detailed Solution Below)

Option 1 : {1, 4}
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Detailed Solution

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The correct answer is {1, 4}

SOLUTION:

X= {1 ≤ n ≤ 8} So, X = {1, 2, 3, 4, 5, 6, 7, 8}

P= "n is an even integers" So, P = {2, 4, 6, 8}

Q = "(3 ≤ n ≤ 7) ^ (n ≠ 6)" So, Q = {3, 4, 5, 7}

P ↔ Q = (¬P v Q)  ^ (P v ¬Q)

P ↔ Q = ({1, 3, 5, 7} v {{3, 4, 5, 7}) ^ ({2, 4, 6, 8} v {1, 2, 6, 8})

P ↔ Q = {1,3, 4, 5, 7} ^ {1, 2, 4, 6, 8}

P ↔ Q = {1, 4}

So, Correct answer is Option 1 {1, 4}

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