# Problem 1008

Let p and q represent the following simple statements:

p :  A basketball is round.

q :  A hockey stick is round.

Write the following compound statement in its symbolic form.

A basketball is round and a hockey stick is not round.

Solution:-

The given compound statement is a conjunction. A conjunction is a compound statement formed by joining two simple statement with the connective and.

“A basketball is round ” is the first simple statement in the conjunction; it preceded the connective and.

This simple statement is represented by the letter p.

“A hockey stick is not round” is the second simple statement in the conjunction; it follows the connective and.

Notice that this is the negation of the statement  ”A hockey stick is round,” represented by q.

The symbolic form of the statement “A hockey stick is not round” is   ̴q.

The symbol that represents the connective and is Λ .

To write the conjunction in symbolic form, replace each simple statement with its symbolic form. Then replace the connective and with the symbol that represent it.

A basketball is round and a hockey stick is not round.

p    Λ       ̴q

The symbolic form of the conjunction is p Λ   ̴q