Answer to Question #261268 in Discrete Mathematics for ifti

Question

Let p and q be the propositions

p : It is below freezing. (including negations).

q : It is snowing

Write these propositions using p and q and logical connectives

a) It is below freezing and snowing.

b) It is below freezing but not snowing.

c) It is not below freezing and it is not snowing.

d) It is either snowing or below freezing (or both).

e) If it is below freezing, it is also snowing.

f ) Either it is below freezing or it is snowing, but it is

not snowing if it is below freezing.

Answer 1

a) It is below freezing and snowing.

$p \wedge q$

b) It is below freezing but not snowing.

$p \wedge \overline q$

c) It is not below freezing and it is not snowing.

$\overline p \wedge \overline q$

d) It is either snowing or below freezing (or both).

$p \vee q$

e) If it is below freezing, it is also snowing.

$p \to q$

f ) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing.

$\left( {p \vee q} \right) \wedge \left( {p \to \overline q } \right)$