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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 :
If question paper is not hard then I will pass in the examination.

Text Solution

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The correct Answer is:
To translate the given sentence "If question paper is not hard then I will pass 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 Statements**: - The negation of \( p \) (question paper is not hard) is represented as \( \neg p \). - To express "I will pass in the examination," we need to negate \( q \). The negation of \( q \) (I will not fail in the examination) is represented as \( \neg q \). 3. **Construct the Conditional Statement**: - The sentence "If question paper is not hard then I will pass in the examination" can be written in logical form as: \[ \neg p \implies \neg q \] - Here, \( \implies \) represents the logical implication "if...then." ### Final Translation: Thus, the translation of the sentence into symbols is: \[ \neg p \implies \neg q \]
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