# Equivalents to Given Statements

Can you give an equivalent statement to

1. If an Iowa farmer does not grow corn or beans, then he grows alfalfa.

2. It is not true that both Baghdad and Iraq are countries.

3. If my nephew is playing BB tonight, then I am going to the game.

Â© BrainMass Inc. brainmass.com October 3, 2022, 12:56 am ad1c9bdddfhttps://brainmass.com/math/consumer-mathematics/equivalents-given-statements-468495

## SOLUTION This solution is **FREE** courtesy of BrainMass!

These statements can be written using logical connectives.

The following symbols are typically used:

~ means negation

^ means 'and' and is a conjunction connective

V means 'or" and is a disjunction

--> is an "if, then" statement.

Typically we use parenthesis around the connectives that appear together on one side of a comma.

Here are the translations for your three combined statements.

1.

Let p: Iowa farmer grows corn

Let q: Iowa farmer grows beans

Let r: Iowa farmer grows alfalfa

The statement: If an Iowa farmer does not grow corn or beans, then he grows alfalfa.

Translates to: ~(p V q) --> r

2.

Let p: Baghdad is a country

Let q: Iraq is a country

The statement: It is not true that both Baghdad and Iraq are countries.

Translates to: ~(p ^ q)

3.

Let p: My nephew is playing BB tonight

Let q: I am going to the game

The statement: If my nephew is playing BB tonight, then I am going to the game

Translates to: p --> q

https://brainmass.com/math/consumer-mathematics/equivalents-given-statements-468495