Q:

Given the statement "If I have the disease, then I will test positive." Show all work. (Discrete Mathematics)a) Write the converse.b) Write the inverse.c) Write the contrapositive.d) Write the statement as a disjunction.e) Write the negation.

Accepted Solution

A:
Answer:a) if I test positive, then I will have the diseaseb) if I don't have the disease, then I won't test positivec) if I don't test positive, then I won't have the diseased) either I don't have the disease or I will test positivee) I have the disease and I won't test positive.Step-by-step explanation:Having the statement: if m, then n.a) the converse will be:if n, then m.m= I have the diseasen= I (will) test positive.converse: if I test positive, then I (will) have the disease.(It doesn't have to be true always).b) the inverse will be:if not m, then not n.inverse: if I don't have the disease, I won't test positive.c) the contrapositive will be:if not n, then no m.contrapositive: if I don't test positive, then I (will) not have the disease.(It doesn't have to be true always).d) disjunction:We can rewrite if m, then n as: m⇒n, the disjunction will be:m⇒n ≡ ¬m ∨ n (not m or n).disjunction: either I don't have the disease or I will test positive.e) negation:the negation of m⇒n is ¬(m⇒n) ≡ ¬(¬m ∨ n) ≡ m∧¬n.negation: I have the disease and I won't test positive.I have the disease but I won't test positive.(this is the only statement completely false).