- 2074 Bhadra · 3 marks
Converse etc. of temple statement
Short answer
Let p: I visit temple, q: it's Saturday. The statement 'p only if q' is p→q. Converse: q→p (If Saturday, I visit). Inverse: ¬p→¬q (If I don't visit, it's not Saturday). Contrapostive: ¬q→¬p (If not Saturday, I don't visit).
Write the inverse, converse and contrapositive of the statement "I visit temple only if it's Saturday".
Let p: "I visit the temple" and q: "it is Saturday". "p only if q" means p → q: if I visit the temple, then it is Saturday.
| Form | Symbolic | Statement |
|---|---|---|
| Converse | q → p | If it is Saturday, then I visit the temple. |
| Inverse | ¬p → ¬q | If I do not visit the temple, then it is not Saturday. |
| Contrapositive | ¬q → ¬p | If it is not Saturday, then I do not visit the temple. |
Only the contrapositive is logically equivalent to the original statement.
✓ Answer checked by Claude Opus 5.5 (high effort)
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