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Consider the following: p : Question p...

Consider the following:
p : Question paper is hard.
q : I will fail in the examination.
Then translate the following sentence into symbols :
Question paper is not hard if and only if I will fail in the examination.

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The correct Answer is:
To translate the given sentence "Question paper is not hard if and only if I will fail in the examination" into symbols, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Statements**: - Let \( p \): "Question paper is hard." - Let \( q \): "I will fail in the examination." 2. **Negate the First Statement**: - The phrase "Question paper is not hard" can be represented as \( \neg p \) (the negation of \( p \)). 3. **Understand the "if and only if" (iff)**: - The phrase "if and only if" indicates a biconditional relationship. In logical symbols, this is represented as \( \iff \). 4. **Construct the Biconditional Statement**: - The complete statement "Question paper is not hard if and only if I will fail in the examination" can be expressed as: \[ \neg p \iff q \] ### Final Answer: The symbolic representation of the statement is: \[ \neg p \iff q \]
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