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Write 'T' for True and 'F' for False.
The negation of `p implies q` is `p ^^ ~| q`.

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To determine the truth value of the statement "The negation of `p implies q` is `p conjunction negation q`", we will analyze it step by step. ### Step-by-Step Solution: 1. **Understanding the Implication**: The implication `p implies q` can be expressed in logical terms as: \[ p \implies q \equiv \neg p \lor q \] This means that "if p is true, then q is also true" can be rewritten as "either p is false or q is true". **Hint**: Remember that an implication can be rewritten using negation and disjunction. 2. **Negating the Implication**: Now, we need to find the negation of `p implies q`: \[ \neg (p \implies q) \equiv \neg (\neg p \lor q) \] **Hint**: When negating an expression, you can apply De Morgan's Laws. 3. **Applying De Morgan's Laws**: According to De Morgan's Laws, the negation of a disjunction is the conjunction of the negations: \[ \neg (\neg p \lor q) \equiv p \land \neg q \] **Hint**: De Morgan's Laws help in transforming negated expressions. 4. **Comparing with the Given Statement**: We have derived that: \[ \neg (p \implies q) \equiv p \land \neg q \] The statement we need to evaluate is whether this is equivalent to `p conjunction negation q`, which is also written as: \[ p \land \neg q \] **Hint**: Check if both expressions are identical. 5. **Conclusion**: Since we have shown that the negation of `p implies q` is indeed `p conjunction negation q`, we conclude that the statement is true. Therefore, the truth value of the statement is: \[ \text{T (True)} \] ### Final Answer: T (True)
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ML KHANNA-MATHEMATICAL REASONING-PROBLEM SET (1)(TRUE OR FALSE)
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  5. Write 'T' for True and 'F' for False. "If you read" then you will p...

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  6. Write 'T' for True and 'F' for False. ~| (p implies q)=p ^^ ~| q.

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  7. Write 'T' for True and 'F' for False. (p vv q) ^^ q = p.

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  8. Write 'T' for True and 'F' for False. (p vv q) ^^ p =p is an absorpt...

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  9. Write 'T' for True and 'F' for False. (p hArr q) hArr (p implies q) ...

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  10. Write 'T' for True and 'F' for False. If p is false and q is true, ...

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  11. Write 'T' for True and 'F' for False. Always true statement is calle...

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  12. Write 'T' for True and 'F' for False. 1 stands for true and 0 stands...

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  13. Write 'T' for True and 'F' for False. If (p ^^ q) implies r in this ...

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  14. Write 'T' for True and 'F' for False. If p -= q, then p hArr q will ...

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  15. Write 'T' for True and 'F' for False. p vv (q ^^ r) -= (p vv q) ^^ (...

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  16. Write 'T' for True and 'F' for False. ~| (p hArr q) -= p hArr ~| q -...

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  17. Write 'T' for True and 'F' for False. (p implies q) vv (r implies p)...

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  18. Write 'T' for True and 'F' for False. (p vv q) ^^ r is a dual of (p ...

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  19. Write 'T' for True and 'F' for False. (p ^^ q) implies q is not taut...

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  20. Write 'T' for True and 'F' for False. ~| (p implies q) vv r is a dua...

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