Chapter 2 Reasoning and Proofs

Front

What is the contrapositive of the statement: 'If a polygon is a quadrilateral, then it is a trapezoid'?

Back

If a polygon is not a trapezoid, then it is not a quadrilateral.

Front

What property justifies the statement: 'If x - 5 = 6, then x = 11'?

Back

Addition Property of Equality.

Front

Identify the conclusion in the statement: 'If I have a Siberian Husky, then I have a dog.'

Back

I have a dog.

Front

What is step 4 in solving the equation x - 5 = 6?

Back

Addition property of equality.

Front

What is the negation of the statement: 'I don't like brussel sprouts'?

Back

I like brussel sprouts.

Front

Define a conditional statement.

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions.

Front

What is the converse of a statement?

Back

The converse of a statement 'If p, then q' is 'If q, then p'.

Front

What is the inverse of a statement?

Back

The inverse of a statement 'If p, then q' is 'If not p, then not q'.

Front

Explain the Law of Syllogism.

Back

If 'If p, then q' and 'If q, then r' are true, then 'If p, then r' is also true.

Front

What is a biconditional statement?

Back

A biconditional statement is true if both the conditional and its converse are true, expressed as 'p if and only if q'.