Problem 1009

Let p, q, and r represent the following simple statements:

p: I lie on the sofa.

q: I take a nap.

r: I go jogging.

Write the following compound statement in its symbolic form.

I lie on the sofa and I take a nap, or I go jogging.

Solution:-

First, notice that this statement contains more than one connective.

I lie on the sofa and I take a nap, or I go jogging.

When compound statement containing more than one connective are expressed in words, commas are used to indicate which simple statement are to be grouped together.

Two simple statement that appear on the same side of a comma are grouped together in parentheses when the statement is written symbolically.

Since the compound statement.

I lie on the sofa and I take a nap appears to the left of the comma, the symbolic statement representing it is grouped within parentheses.

The symbolic statement expressing

I lie on the sofa and I take a nap

Is (p  Λ  q).

Next , write the symbol that represents the connective. Then symbolically write the statement the follows the connective.

I lie on the sofa and I take a nap, or I go jogging.

(p Λ q) V r

The symbolic form of the compound statement

I lie on the sofa and I take a nap, or I go jogging.

Is (p Λ q) V r.

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