Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11
Question:
The contrapositive of the statement "If two triangles are identical, then they are similar" is
If two triangles are not similar, then they are not identical
If two triangles are not identical, then they are not similar
If two triangles are not identical, then they are similar
If two triangles are not similar, then they are identical
Step-by-Step Solution
Key Concept: A disjunction is true if at least one of its disjuncts is true; material conditional equivalence $p \rightarrow q \equiv \neg p \vee q$.
Let $p: 2 + 2 = 4$ (true statement), $q$: India is a country (true statement). The given statement is $\neg p \vee q$. Since $p$ is true, $\neg p$ is false. Since $q$ is true, the disjunction $\neg p \vee q$ is true. Therefore $p \rightarrow q \equiv p \vee q$ is true.
Correct Answer: F