Answer
Verified
424.8k+ views
Hint- This question is solved by making truth table of $p,{\text{ }}q,{\text{ }}r,{\text{ }} \sim r,{\text{ }}\left( {p \wedge q} \right){\text{ and }}\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$.
Now given that,
$\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$
Now we have to find the truth values of $p,q{\text{ and }}r$
We will find that by using truth table,
Now the possible combinations are ${2^3} = 8$ (Because variables are three.)
Also we know that,
$
\sim {\text{ means }}NOT \\
\wedge {\text{ means }}AND \\
\vee {\text{ means }}OR \\
$
$
p{\text{ }}q{\text{ }}r{\text{ }} \sim r{\text{ }}\left( {p \wedge q} \right){\text{ }}\left( {p \wedge q} \right) \vee \left( { \sim r} \right) \\
T{\text{ }}T{\text{ }}T{\text{ }}F{\text{ }}T{\text{ }}T \\
F{\text{ }}T{\text{ }}T{\text{ }}F{\text{ }}F{\text{ }}F \\
T{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}F{\text{ }}F \\
F{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}F{\text{ }}F \\
T{\text{ }}T{\text{ }}F{\text{ }}T{\text{ }}T{\text{ }}T \\
F{\text{ }}T{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}T \\
T{\text{ }}F{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}T \\
F{\text{ }}F{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}T \\
$
Now it is given that $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$ and we have to find the values of $p,q{\text{ and }}r$
when $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$.
Now, from the truth table, we will see the respective values of $p,q{\text{ and }}r$ for $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$.
Therefore, the values of $p,q{\text{ and }}r$ are $F,F,T$ respectively.
Thus, the correct option is (E).
Note- Whenever we face such types of questions the key concept is that we should solve it by using a truth table. In this question we find the values of $p,q{\text{ and }}r$ by making the truth table and then we see the respective values of $p,q{\text{ and }}r$ for $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$.
Now given that,
$\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$
Now we have to find the truth values of $p,q{\text{ and }}r$
We will find that by using truth table,
Now the possible combinations are ${2^3} = 8$ (Because variables are three.)
Also we know that,
$
\sim {\text{ means }}NOT \\
\wedge {\text{ means }}AND \\
\vee {\text{ means }}OR \\
$
$
p{\text{ }}q{\text{ }}r{\text{ }} \sim r{\text{ }}\left( {p \wedge q} \right){\text{ }}\left( {p \wedge q} \right) \vee \left( { \sim r} \right) \\
T{\text{ }}T{\text{ }}T{\text{ }}F{\text{ }}T{\text{ }}T \\
F{\text{ }}T{\text{ }}T{\text{ }}F{\text{ }}F{\text{ }}F \\
T{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}F{\text{ }}F \\
F{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}F{\text{ }}F \\
T{\text{ }}T{\text{ }}F{\text{ }}T{\text{ }}T{\text{ }}T \\
F{\text{ }}T{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}T \\
T{\text{ }}F{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}T \\
F{\text{ }}F{\text{ }}F{\text{ }}T{\text{ }}F{\text{ }}T \\
$
Now it is given that $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$ and we have to find the values of $p,q{\text{ and }}r$
when $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$.
Now, from the truth table, we will see the respective values of $p,q{\text{ and }}r$ for $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$.
Therefore, the values of $p,q{\text{ and }}r$ are $F,F,T$ respectively.
Thus, the correct option is (E).
Note- Whenever we face such types of questions the key concept is that we should solve it by using a truth table. In this question we find the values of $p,q{\text{ and }}r$ by making the truth table and then we see the respective values of $p,q{\text{ and }}r$ for $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE