Question

Given below are three conditions for discrete mathematics:

A: If $2+4=7$, then $3+4=8$

B: if $3+5=8$, then the earth is flat

C: if $A$ and $B$ are true, then $5+4=11$.

Choose the correct option.

• A. $A$ is true, $B$ and $C$ are false
• B. $B$ is true, $A$ and $C$ are false
• C. $C$ is true, $A$ and $B$ are false
• D. $B$ is false, $A$ and $C$ are true

Answer 1

The correct option is D

$B$ is false, $A$ and $C$ are true

Step1: Given data and assumptions.

Three given conditions $A$, $B$ and $C$.

Let $p$ and $q$ be the propositions relation of the given condition.

Step2: Construct a truth table for $\left(p\to q\right)$.

We know that,

p	q	$\left(p\to q\right)$
T	T	T
T	F	F
F	T	T
F	F	T

As compare the truth table of $p$ and $q$ with the given conditions $A$, $B$ and $C$ we get.

$A$ is true, $B$ is false, $C$ is true.

Hence, option D is correct.