Question

The negation of the statement “If $5<7$ and $7>2$, then $5>2$” is

• A. $5<7$ and $7>2$ and $5\le2$
• B. $5<7$ and $7>2$ or $5<2$
• C. $5<7$ and $7>2$ and $5>2$
• D. $5<7$ and $7>2$ or $5\le2$

Hint:

The negation of “If $p$ then $q$” is “$p$ and not $q$”.

Answer 1

The Correct Option is A

Step 1: Writing the statement symbolically.
Let \[ p: (5<7 \land 7>2), \quad q: (5>2) \] The given statement is $p \Rightarrow q$. 
Step 2: Using negation rule. 
The negation of $p \Rightarrow q$ is \[ p \land \neg q \] 
Step 3: Writing the negation explicitly. 
\[ (5<7 \land 7>2) \land (5\le2) \] 
Step 4: Conclusion. 
The correct negation is option (A).