Question

. Let p and q be the propositions p: He is rich q: He is happy Write the following propositions using p and q and logical connectives.

a. If he is rich, then he is unhappy.

b. He is neither rich nor happy.

c. It is necessary to be poor, in order to be happy.

d. He is either rich or happy (or both).

Answer 1

Solution:

p: He is rich

q: He is happy

a. If he is rich, then he is unhappy.

$p\rightarrow q$

b. He is neither rich nor happy.

$\sim p\wedge \sim q$

c. It is necessary to be poor, in order to be happy.

$\sim p\leftrightarrow q$

d. He is either rich or happy (or both).

$p∨q$