Question

In: Advanced Math

1) Consider the statement: “If it snows then we will stay home”. Find the: Converse Inverse...

1) Consider the statement: “If it snows then we will stay home”. Find the:

Converse

Inverse

Contra-positive

Assuming the original statement is true, which statements must also be true?

Determine if the statement is true or false and provide a counter-example for the false statements.

The sum of two integers is an integer.

Prime numbers are odd.

The product of two irrational numbers is irrational.

The sum of a rational number and an irrational number is irrational.

Solutions

Expert Solution

(1)

(a)

Given statement:   "If it snows, then we will stay home"

Converse:

If we will stay home, then it snows."

Explanation:

Converse is the switching the hypothesis and conclusion of a conditional statement.

(b)

Given statement:   "If it snows, then we will stay home"

Inverse:

If it does not snow, then we will not stay home

Explanation:

Inverse of a conditional statement is when both the hypothesis and conclusion are negated.

(c)

Given statement:   "If it snows, then we will stay home"

Contra - positive:

If we will not stay home, then it does not rain.

Explanation:
Contra - positive is switching the hypothesis and conclusion of a conditional statement and negating both.

(d)

Assuming the original statement is true, (c) Contra - positive statement must also be true.

Explanation:

The contra - positive of any true proposition must also be true.

(2)

(a)

The sum of two integers is an integer. : True

(b)

Prime numbers are odd. : False

Counter example: 2 is a prime number. It is even.

(c)

The product of two irrational numbers is irrational. : False

Counter example: is irrational. But is rational number

(d)

The sum of a rational number and an irrational number is irrational.   True

Colby Messinger answered 1 year ago
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