Let p and q be the propositions . p: we are going to make a cheaper phone ; q: w

Question

Let p and q be the propositions .

p: we are going to make a cheaper phone ; q: we are going to lose business. Translate the following into symbolic form.

a.) If we make a cheaper phone, then we will lose business .

b.) If we lose business, then we will make a cheaper phone.

c.) We will lose business if and only if we make a cheaper phone.

d.) If we lose business, then we will not make a cheaper phone.

e.) It is not the case that we will lose business if and only if we do not make a cheaper phone. ,

Explanation / Answer

A) Answer pq

Explanation-

If p,q are both propositions,
then so is“if p then q.”
Even though there are two
words (“if”, “then”), we use
one symbol, namely . So “if p
then q” is written “pq.”
“pq” is also pronounced as
“p implies q.” Some authors

B) Answer qp

Explanation-

this statement is reverse statement of A.

C) Answer qp

Explanation-

If p,q are both propositions, then
so is “p if and only if q.”
Sometimes this is abbreviated
“p iff q.”
Intuitively, this means that p is
true precisely in the same
circumstances as q.

D) Answer q¬ p

Explanation-

¬ symbol is used for negation of a statement

E) Answer-   ¬(q ¬p)

Explanation-

This statement is combination of negation,if and only if type statement.See Above C and D.

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