Question

A.         Let p and q be propositions

p: 4 is an even integer

q: 5 is an odd integer

 

Write each of the following sentences in terms of p, q and logical connectives:

______________1. 4 is an even integer and 5 is an odd integer.

______________2. 4 is not an even integer or 5 is an odd integer.

______________3. If 4 is an even integer then 5 is an odd integer.

______________4. 4 is an even integer whenever 5 is an odd integer.

______________5. 4 is not an even integer if an only if 5 is not an odd integer.

Answer 1

______________1. 4 is an even integer and 5 is an odd integer: $p \wedge q$

______________2. 4 is not an even integer or 5 is an odd integer: $\neg p \vee q$

______________3. If 4 is an even integer then 5 is an odd integer: $p \to q$

______________4. 4 is an even integer whenever 5 is an odd integer: $q \to p$

______________5. 4 is not an even integer if an only if 5 is not an odd integer: $\neg p \leftrightarrow \neg q$