Answer to Question #245878 in Discrete Mathematics for dev

Question

3.State the converse, contrapositive and inverse of the conditional statement: When it’s

hot out, it is necessary that I eat ice cream.

4. Steve, Bill and Larry go to a bar. The bartender asks: “Does everyone want beer?”

Steve says: “I don’t know.” Bill says: “I don’t know.” Finally Larry says: “No, not

everyone wants beer.” The bartender proceeds to serve beer to those among these three

who want it. How did he figure out who wanted beer?

5. Show that ¬p → (q → r) and q → (p∨r) are logically equivalent, in two different ways:

(i) use a truth table, (ii) without using truth tables.

Answer 1

3.

converse: if it’s hot out, then I eat ice cream

contrapositive: if it is not hot out, then I do not eat ice cream

inverse: if I do not eat ice cream, it is not hot out

5.

i)

$q → (p∨r)\equiv (q\to p)\lor (q\to r)\equiv ¬p → (q → r)$

ii)

4.

Since Larry says: “No, not everyone wants beer”, he does not want beer. So, Steve and Bill want beer.