Answer
Verified
480.9k+ 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
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE