     Question Answers

# 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  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.
View Notes
Truth Table  BE Full Form  Use of If Then Statements in Mathematical Reasoning  Log Values From 1 to 10  Who will be Ningthou - Summary  Should Plastic Be Banned Essay  D and F Block Catalyst  The D- and F- Block Elements  Difference Between B cells and T cells  T-Distribution  