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# Determine whether these biconditionals are true or ## Problem 16E Chapter 1.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 16E

Determine whether these biconditionals are true or false.

a) 2 + 2= 4 if and only if 1 + 1 = 2.

b)1 +1 = 2 if and only if 2 + 3 = 4.

c)1 + 1 = 3 if and only if monkeys can fly.

d) 0 > 1 if and only if 2 > 1.

Step-by-Step Solution:

Step 1:

In this problem we have to determine the given biconditional statements are true or false.

Definition of biconditional :

If both parts having same truth value then biconditional statement  is true . the biconditional operator is denoted by . the biconditional p q  represents “ p if and only if q. “

Table of biconditional :

 p q p q T T T T F F F T F F F T

Step 2:

a:

Let 2 +2 = 4 is p statement and 1+1 = 2 is q statement .

Clearly p statement is true and q statement is also true.

Hence p q is true

Consequently 2 + 2= 4 if and only if 1 + 1 = 2 is TRUE  statement.

Step 3:

b:

Let 1 +1 = 2 is p statement and  2 + 3 = 4 is q statement .

Clearly  p statement  is true and q statement is false , so according to the table p q is false.

Consequently 1 +1 = 2 if and only if 2 + 3 = 4 is FALSE statement.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073383095

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Determine whether these biconditionals are true or

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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 1.1 - Problem 16e