# The truth values of $p,q{\text{ and }}r$ for which $\left( {p \wedge q} \right) \vee \left( { \sim r} \right)$ has truth values $F$ are respectively

A.$F,T,F$

B.$F,F,F$

C.$T,T,T$

D.$T,F,F$

E.$F,F,T$

Answer

Verified

385.5k+ 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

Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts

Which of the following Chief Justice of India has acted class 10 social science CBSE

Green glands are excretory organs of A Crustaceans class 11 biology CBSE

What if photosynthesis does not occur in plants class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

10 slogans on organ donation class 8 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE