Write the negation of the following statement:
$p:$ For every positive real number $x,$ the number $x-1$ is also positive.

The number of choices of $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$,such that $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$ is a tautology,is

State whether the "Or" used in the following statement is "exclusive" or "inclusive". Give reasons for your answer.
To apply for a driving licence,you should have a ration card or a passport.

The missing value in the following figure is

The last column in the truth table of the statement pattern $[p \rightarrow (q \wedge \sim p)] \vee [(p \vee \sim q) \wedge p]$ is

If $p, q, r, s$ are statements,where:
$p: A^2-B^2=(A-B)(A+B)$ where $A, B$ are matrices and $AB \neq BA$
$q: 5 \leqslant 5$
$r: { }^8 C_1+{ }^8 C_2+{ }^8 C_3+\ldots+{ }^8 C_8=256$
$s: \text{Maximum value of } { }^8 C_r \text{ is } 70$
Which of the following statements has a truth value of true?