discrete mathematics for a computer programming course Let p

(discrete mathematics for a computer programming course)

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

Solution

Answer:

a) p ---> q

b) q--->p

c) q <----> p

d) q ---> ~p

e ) ~q <----> ~p

Here two operations of a discrete maths are used :

-- Implication

--Bi -implication

Implication (--->) : says if one statement is true , then other is true also

Bi - implication (<--->) :says first statement is true if and only if second startement is true

Negation (~) : simply complement.