Check whether the following statement is true | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the statements be defined as follows:$p: xy$ is odd.$q:$ Both $x$ and $y$ are odd.We need to verify the implication $p \Rightarrow q$ by check

Vedclass · Accepted Answer

True

Vedclass · Answer

(A) Let the statements be defined as follows:$p: xy$ is odd.$q:$ Both $x$ and $y$ are odd.We need to verify the implication $p \Rightarrow q$ by checking its contrapositive statement,which is $\sim q \Rightarrow \sim p$.$\sim q:$ It is false that both $x$ and $y$ are odd. This means at least one of $x$ or $y$ is even.Let $x = 2n$ for some integer $n \in \mathbb{Z}$.Then $xy = (2n)y = 2(ny)$,which is an even number.Thus,$\sim p$ is true (i.e.,$xy$ is even).Since $\sim q \Rightarrow \sim p$ is true,the original statement $p \Rightarrow q$ is true.

Check whether the following statement is true or false by proving its contrapositive: If $x, y \in \mathbb{Z}$ such that $xy$ is odd,then both $x$ and $y$ are odd.

Similar Questions

Consider the following three statements:
$P: 5$ is a prime number.
$Q: 7$ is a factor of $192$.
$R: \text{L.C.M. of } 5 \text{ and } 7 \text{ is } 35$.
Then,the truth value of which one of the following statements is true?

Among the statements:
$(S1) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow ( p$ $\Rightarrow r )$
$(S2) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow (( p$ $\Rightarrow r ) \vee ( q$ $\Rightarrow r ))$

Which of the following is an open statement?

If $S^(p, q, r)$ is the dual of the compound statement $S(p, q, r)$ and $S(p, q, r) = \sim p \wedge [\sim (q \vee r)]$,then $S^(\sim p, \sim q, \sim r)$ is equivalent to:

If the truth value of the expression $[(p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r)]$ $\rightarrow (p \wedge q)$ is False,then the truth values of $p, q, r$ are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module