Question 1 :
If $p:3$ is a prime number and $q:$ one plus one is three, then the compound statement "It is not that $3$ is a prime number or it is not that one plus one is three" is

Question 2 :
Determine whether the following compound statements are true or false:<br/>Delhi is in India and $2+2=4$

Question 3 :
Let $f$ be a function from a set $X$ to a set $Y$.<br/>Consider the following statements<br/>$P:$ For each $x\epsilon X$, there exists unique $y\epsilon Y$ such that $f(x) = y$.<br/>$Q:$ For each $y\epsilon Y$, these exists $x\epsilon X$ such that $f(x) = y$.<br/>$R:$ There exist $x_{1}, x_{2}\epsilon X$ such that $x_{1}\neq x_{2}$ and $f(x_{1}) = f(x_{2})$<br/>The negation of the statement $&#34;f$ is one-to-one and onto&#34; is

Question 4 :
The negative of the statement "If a number is divisible by $15$ then it is divisible by $5$ or $3$"

Question 7 :
If $p, q, r$ are simple proportions with truth values $T, F, T$, then the truth value of $(\sim p\vee q)\wedge \sim r \Rightarrow p$ is

Question 9 :
The truth values of p, q and r for which $(p \wedge q) \vee (\sim r)$ has truth value F are respectively

Question 10 :
"If natural numbers are whole numbers, then rational numbers are integers" or "If rational numbers are integers, then natural numbers are whole numbers" <span>is</span>

Question 12 :
Write the compound statement, "If p, then q and if q, <span>then p" in symbolic form.</span>

Question 13 :
Assertion: (A): Let $\displaystyle P(n)=111\dots1 (91$ times$)$, then $P(n)$ is a prime number. Reason: (R): Every prime number has at most and at least two factors.

Question 14 :
Which of the following is logically equivalent to $\displaystyle \sim \left (\sim p\rightarrow q\right )$?

Question 15 :
Consider the following statements<br>$P:$Suman is brilliant<br>$Q:$Suman is rich<br>$R:$Suman is honest.<br>The negative of the statement."Suman is brilliant and dishonest, if and only if Suman is rich" can be expressed as

Question 16 :
"If A is true, then B is false", is logically equivalent to which of the following?<br>I. If A is false, then B is true.<br>II. If B is false, then A is true.<br>III. If B is true, then A is false

Question 18 :
Consider the statements<span> <br>(i)Two plus three is five.<br>(ii) Every square is a rectangle.<br>(iii) Sun rises in the east.<br>(iv) The earth is not a star. <br><span>Which of the above statements have truth value (T) ?<br></span></span>

Question 20 :
<span>Choose the conclusion of given statements:</span><div><br/></div><div>All scientists working in America are talented. Some Indian scientists are working in America. Therefore, &#34;Some Indian scientists are talented.&#34;<br/></div>

Question 21 :
The statement "If $2^2 = 5$ then I get first class" is logically equivalent to

Question 22 :
The inverse of: &#34;If two triangle are congruent then they are similar&#34; is<br/>

Question 23 :
If $P(n)$ be the statement $n(n+1)+1$ is odd, then which of the following is false?<br>

Question 24 :
The truth value of the statement, "We celebrate our <span>Independence day on 15 August", is</span>

Question 25 :
Let<br>p : Boys are playing<br>q : Boys are happy<br>the equivalent form of compound statement of $\displaystyle p\rightarrow q$ is<br>