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