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 pq represents “ p if and only if q. “

Table of biconditional :

p |
q |
pq |

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.