Tag: implications

Question 1

Without using truth , whether
$\left[ {p\Delta \left( { \sim q\Delta r} \right)} \right]V\left[ { \sim r\Delta \sim q\Delta p} \right] \equiv p$

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

True
False

Answer

Correct Option: B

Question 2

Solve it:-
$\left( {p \to q} \right) \to [\left( { \sim p \to q} \right) \to q]$

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

Tautology
Contradiction
Contingent
Not statement

Explanation:

$Y=\left( p\longrightarrow q \right) \longrightarrow \left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$

Method : TRUTH TABLE [ ALWAYS PREFERABLE]

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

As the result is always TRUE $\left(i.e. 1\right)$;

$\left( p\longrightarrow q \right)\longrightarrow \left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$ is Tautology.

A. Tautology

Answer

Correct Option: A

Question 3

Which of the following is true

maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$a _{r}=a _{n-r}$
$a _{2r}=a _{n-r}$
$a _{r}=a _{2n-r}$
$None\ of\ these$

Answer

Correct Option: A

Question 4

Let $p$ and $q$ be two propositions given by
$p$ : The sky is blue.
$q$ : The milk is white.
Then $p\wedge q$ will be

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

The sky if blue or milk is white
The sky is blue and milk is white
The sky is white and milk is blue
If the sky is blue then milk is white

Answer

Correct Option: B

Question 5

Let $p$ and $q$ be two propositions. Then the contrapositive the implication $p\rightarrow q$

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

$\sim q\rightarrow \sim p$
$\sim p\rightarrow \sim q$
$q\rightarrow p$
$p\leftrightarrow q$

Answer

Correct Option: A

Question 6

Negation of $(\sim p\rightarrow q)$ is ________________.

business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$\sim { p }{ \wedge }\sim q$
$\sim \left( p\vee q \right) \vee \left( p\vee \left( \sim p \right) \right) $
$\sim \left( p\vee q \right) \wedge \left( p\vee \left( \sim p \right) \right) $
$\left( \sim p\vee q \right) \wedge \left( p\vee \sim q \right) $

Answer

Correct Option: A

Question 7

$p \wedge ( q \vee \sim p ) =?$

business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$p \vee q$
$p \wedge q$
$p \rightarrow q$
none of these

Answer

Correct Option: B

Question 8

$( p \wedge q ) \vee ( \sim p \wedge q ) \vee ( \sim q \wedge r ) =? $

business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$q \vee r$
$q \wedge r$
$q \rightarrow r$
none of these

Answer

Correct Option: B

Question 9

If $p$ is false, $q$ is true, then which of the following is/are false?

maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$\sim (p\Rightarrow q)$
$\sim p$
$\sim p\Rightarrow q$
$\sim q$

Explanation:

$p$	$q$	$p\Rightarrow q$	$\sim \left( p\Rightarrow q \right) $	$\sim p$	$\sim q$	$\sim p\Rightarrow q$
F	T	T	F	T	F	T

Here we see that $\sim \left( p\Rightarrow q \right) $ and $\sim q$ are false

Answer

Correct Option: A,D

Question 10

$p$: He is hard working.
$q$: He is intelligent.
Then $ \sim q\Rightarrow\sim p$, represents

business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

If he is hard working, then he is not intelligent.
If he is not hard working, then he is intelligent.
If he is not intelligent, then he is not had working.
If he is not intelligent, then he is hard working.

Answer

Correct Option: C

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

Tag: implications

Questions Related to implications

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$