Tag: business maths

Question 1

The proposition $\left( {p \wedge q} \right) \Rightarrow p$ is

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

neither tautology nor contradiction
A tautology
A contradiction
Cannot be determined

Answer

Correct Option: B

Question 2

The statement $p \to (q \to p)$ is equivalent to

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$p \to q$
$p \to (q \vee p)$
$p \to (q \to p)$
$p \to (q \wedge p)$

Answer

Correct Option: B

Question 3

Which of the following is correct?

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$(~p \vee ~q) \equiv (p \wedge q)$
$(p \rightarrow q) \equiv (~q \rightarrow ~p)$
$~(p \rightarrow ~q) \equiv (p \wedge ~q)$
$~(p \leftrightarrow q) \equiv (p \rightarrow q) \wedge (q \rightarrow p)$

Explanation:

$~(p \leftrightarrow q) \equiv (p \rightarrow q) \wedge (q \rightarrow p)$ is true, we show it by truth table using boolean expression.

1.$p\rightarrow q$=min(1,1+q-p)

2.$p\wedge q$=min(p,q)

3.$p\leftrightarrow q$=1-|p-q|

Now we draw or make truth table using these operations

L.H.S

p	q	$p\leftrightarrow q$
1	1	1
1	0	0

R.H.S

p	q	$p\rightarrow q$	$q\rightarrow p$	$(p \rightarrow q) \wedge (q \rightarrow p)$
1	1	1	1	1
1	1	0	1	0

L.H.S =R.H.S

$~(p \leftrightarrow q) \equiv (p \rightarrow q) \wedge (q \rightarrow p)$

Answer

Correct Option: D

Question 4

$(p \wedge q) \vee \sim p$ is equivalent to

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$\sim p \wedge q$
$\sim p \vee q$
$p \wedge q$
$p \vee q$

Answer

Correct Option: A

Question 5

In a certain code language, $'543'$ means 'give my water'; $'247'$ means 'water is life' and $'632'$ means 'enjoy my life'. Which of the following stands for 'enjoy' in that language?

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$7$
$6$
$2$
$5$

Answer

Correct Option: A

Question 6

$\sim (p \wedge q)\Rightarrow (\sim p)\vee (\sim p \vee q)$ is equal to

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$\sim p \vee q$
$\sim p \wedge q$
$p\vee \sim q$
$p\wedge \sim q$

Answer

Correct Option: A

Question 7

The equivalent of $(p \rightarrow \sim p) \vee (\sim p \rightarrow p)$ is

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$p \vee \sim p$
$T \rightarrow F$
$T \leftrightarrow F$
$p \wedge \sim p$

Answer

Correct Option: A

Question 8

Identify which of the following statement is not equivalent to the others

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

If $x$ is bass then $x$ is bad.
Boss implies bad,
Bad is necessary condition for bass.
$x$ is boss iff $x$ is bad.

Answer

Correct Option: A

Question 9

Either $p$ or $q$ is equivalent to:

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$p \vee q$
$(p \vee \sim q) \vee (q \wedge \sim p)$
$(p \vee \sim q) \wedge (q \vee \sim p)$
none

Answer

Correct Option: A

Question 10

Equivalent statement of ''If $x\in Q$, then $x\in T$'' is
$x\in Q$ is necessary for $x\in l$
$x\in l$ is sufficient for $x\in Q$
$z\in Q$ or $x\in l$
$x\in Q$ but $x\in l$

business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

$I$ & $II$
$I,\ II$ & $IV$
$III$
$All$

Answer

Correct Option: B

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