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Question 1 - If then - Mathematical Reasoning
Last updated at August 14, 2026 by Teachoo
Mathematical Reasoning
Concept wise
- Statements
- Writing negation of statements
- Negation - Checking if true or not
- Finding Compound Statement
- Words 'And' & 'Or'
- Inclusive and exclusive or
- Quantifiers
- Contrapositive and converse
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If then
- If and only if
- Proving not true/false (by giving counter examples)
- Proving True - If and only if
- Proving True - By Contrapositive
- Proving True - By Contradiction
- Necessary and sufficient condition
Transcript
Question 1 Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd. The given statement can be written in five different ways as follows. A natural number is odd implies that its square is odd. (ii) A natural number is odd only if its square is odd. (iii) For the number to be odd, it is necessary that its square is odd. (iv) For the square of a natural number to be odd, it is sufficient that the number is odd. (v) If the square of a natural number is not odd, then the natural number is not odd.
