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Write 'T' for True and 'F' for False. ...

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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Write 'T' for True and 'F' for False. p unless q means ~| q implies p .

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Knowledge Check

  • The negation of p to (-p vee q) is

    A
    `p vee (p vee -q)`
    B
    `p to -(p vee q)`
    C
    `p to q`
    D
    `p wedge -q`
  • The negation of p vv ~ q is

    A
    `~ p ^^ q`
    B
    `p vv ~q`
    C
    `~ p ^^ ~ q`
    D
    `~ p vv ~ q`
  • The dual of p implies q is:

    A
    `~| p vv q`
    B
    `p vv q`
    C
    `p ^^ q`
    D
    `~| p ^^ q`
  • Similar Questions

    Explore conceptually related problems

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

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

    The negation of p to (~p vv q) is

    The inverse of p implies ~| q is :