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Consider the following statements: p ...

Consider the following statements:
p : I shall pass, q : I study
The symbolic represention of the proposition " I shall pass iff I study" is

A

` p toq`

B

`q to p`

C

` p to ~ q`

D

` p harr q`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the symbolic representation of the proposition "I shall pass iff I study," given the statements: - \( p \): I shall pass - \( q \): I study ### Step-by-Step Solution: 1. **Understanding the Proposition**: The phrase "I shall pass iff I study" indicates a biconditional relationship between the two statements \( p \) and \( q \). The term "iff" stands for "if and only if," which means that both statements are equivalent; that is, \( p \) is true if \( q \) is true, and \( p \) is false if \( q \) is false. 2. **Symbolic Representation of Biconditional**: The symbolic representation of the biconditional statement "p iff q" is represented as \( p \iff q \). This notation indicates that both statements \( p \) and \( q \) are true or both are false. 3. **Conclusion**: Therefore, the symbolic representation of the proposition "I shall pass iff I study" is \( p \iff q \). ### Final Answer: The symbolic representation is \( p \iff q \). ---
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