Answer to Question #248557 in Discrete Mathematics for Mj ryem

Question

Q: You do every exercise in the class.
r: You get a 95 in MMW

Write these proposistions symbols using p, q, and r, and logical connectives.
1.You get a 95 in MMW, but you do not do every exercise in the class.
2. You get a 95 on the final examination, you do every exercise in the class and you get 95 in MMW

D.State the converse, inverse and contrapositive of the following propositions.
1. If you will review your lessons, them you will pass MMW.
Converse:
Inverse:
Contrapositive:

2.The beat will sink if it is overloaded
Converse:
Inverse:
Contrapositive:

Answer 1

(a) As i understand, p means "You get a 95 on the final examination"

1. "You get a 95 in MMW, but you do not do every exercise in the class" is $(r\land \lnot q)$
2. You get a 95 on the final examination, you do every exercise in the class and you get 95 in MMW is $(p\land q\land r)$

(b) Let p means "you will review your lessons", q means "you will pass MMW"

So, given statement is $(p\to q)$

Converse: $(q\to p)$ - "if you will pass MMW, them you will review your lessons"

Inverse: $(\lnot p \to \lnot q)$ - "If you will not review your lessons, them you will not pass MMW"

Contrapositive: ($\lnot q \to \lnot p)$ - "If you will not pass MMW, them you will not review your lessons"

(c) Let q means "The beat will sink", p means "it's overloaded"

So, given statement is $(p \to q)$

Converse: $(q\to p)$ - "The beat is overloaded if it will sink"

Inverse: $(\lnot p \to \lnot q)$ - "The beat will not sink if it is not overloaded"

Contrapositive: ($\lnot q \to \lnot p)$ - "if the beat is not overloaded then it will not sink"