Find the component statements of the following and check whether they are true or not.
Chandigarh is the capital of Haryana and $UP$.
Chandigarh is the capital of Haryana and $UP$.
(N/A) The component statements are:
$p:$ Chandigarh is the capital of Haryana.
$q:$ Chandigarh is the capital of $UP$.
The first statement $p$ is true,as Chandigarh is the capital of Haryana.
The second statement $q$ is false,as the capital of $UP$ is Lucknow.
Since the connecting word is 'and',the compound statement is false.
$p:$ Chandigarh is the capital of Haryana.
$q:$ Chandigarh is the capital of $UP$.
The first statement $p$ is true,as Chandigarh is the capital of Haryana.
The second statement $q$ is false,as the capital of $UP$ is Lucknow.
Since the connecting word is 'and',the compound statement is false.
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Similar Questions
For the statements $p$ and $q$,consider the following compound statements :
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
The negation of the statement "If $5 < 7$ and $7 > 2$,then $5 > 2$" is
If $p, q, r, s$ are statements,where:
$p: A^2-B^2=(A-B)(A+B)$ where $A, B$ are matrices and $AB \neq BA$
$q: 5 \leqslant 5$
$r: { }^8 C_1+{ }^8 C_2+{ }^8 C_3+\ldots+{ }^8 C_8=256$
$s: \text{Maximum value of } { }^8 C_r \text{ is } 70$
Which of the following statements has a truth value of true?
$p: A^2-B^2=(A-B)(A+B)$ where $A, B$ are matrices and $AB \neq BA$
$q: 5 \leqslant 5$
$r: { }^8 C_1+{ }^8 C_2+{ }^8 C_3+\ldots+{ }^8 C_8=256$
$s: \text{Maximum value of } { }^8 C_r \text{ is } 70$
Which of the following statements has a truth value of true?
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?
$P: 5$ 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?
DifficultJEE MAIN 2019
View SolutionWhich of the following logical statements is a tautology?
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