Question

1. For each item, write what is required using only English words.

(a) (2 Pts.) The converse, contrapositive, inverse and negation of \If George feels well, then George is is going

to a movie or going dancing".

(b) (2 Pts.) The converse, contrapositive, inverse and negation of \Anna is failing history and psychology,

then Anna is not graduating".

(c) (2 Pts.) The statement represented by the symbols below and the negation of such statement:

8s9c (M(s) ! (D(c) ^ T(s; c)))

where s is a student in York University, c is a class oered in York University, M(s) is the sentence \s is

a Math student", D(c) is the sentence \c is a class in Discrete Mathematics" and T(s; c) is the sentence

\The student s is taking the class c".

Answer 1

c is symbols not clear

Converse, Contrapositive, and Inverse

The converse of the conditional statement is “If Q then P.”

The contrapositive of the conditional statement is “If not Q then not P.”

The inverse of the conditional statement is “If not P then not Q.”

A negation is a statement that cancels out or denies another statement or action.

a)

given

If George feels well, then George is is going to a movie or going dancing.

converse: If george is going to movie or going dancing , then george feels well
contrapositive: If george is not going to movie or not going dancing , then george not feels well
inverse: If george not feel well then george is not going to movie or not going dancing
negative: George feels well and george is going neither to a movie nor not going dancing

b)

Anna is failing history and psychology,then Anna is not graduating

converse: If Anna is not graduating then anna is failing history and psychology
contrapositive: If Anna is graduating, then Anna is not failing history and psychology
inverse: If Anna is not failing history and psychology,then Anna is graduating
negative: Anna is failing history and psychology and Anna is graduating