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# If truth values of p be F and q be T. Then, truth value of $\sim ( \sim p \vee q)$ is equal to A. TB. FC. Either T of FD. Neither T nor F

Last updated date: 12th Jul 2024
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Hint: Let us draw the truth table for different values of p and q. So, we can find the value of a given equation easily.

Now according to the preference order of mathematical reasoning.
Priority goes from left to right in a statement.
And the preference order is
Brackets ( )
Negation $\sim$
And $\wedge$
Or $\vee$
Conditional $\to$
Biconditional $\leftrightarrow$
Now comes the question how to apply these operations. For this we are given with the truth table which states that if p and q are two given conditions and T stands for true and F stands for false then truth table for various values of p and q will be,

 p q $\sim$p $\sim$q p$\wedge$q p$\vee$q p$\to$q p$\leftrightarrow$q T T F F T T T T T F F T F T F F F T T F F T T F F F T T F F T T

Now coming to the problem first we had to solve brackets.
And according to the preference order first we will find the value $\sim p$ in the bracket and after that find the value of $\sim p \vee q$.
So, using truth table if p is F then $\sim p$ will be T
Now we had to find or ($\vee$) of $\sim p$ and q. And it is given in the question that q is T
Using truth table,
Or ($\vee$) of T and T is T.
So, $( \sim p \vee q)$ will be T.
Now finding negation of $( \sim p \vee q)$.
As we know that the value of $( \sim p \vee q)$ is T. So, according to the truth table negation of T will be F.
Hence, the value of $\sim ( \sim p \vee q)$ will be F.
So, the correct option will be B.

Note: Whenever we came up with this type of problem then to find the value of the given statement or equation efficiently first, we had to make a truth table for the given values and then use the preference order defined in mathematical reasoning to solve the equation step by step.