Logic and Proof

Front

What is a hypothesis in a conditional statement?

Back

The hypothesis is the part of a conditional statement that follows 'if'. For example, in 'If I have a Siberian Husky, then I have a dog', the hypothesis is 'I have a Siberian Husky.'

Front

What is the inverse of a conditional statement?

Back

The inverse of a conditional statement 'p → q' is '~p → ~q'. It negates both the hypothesis and the conclusion.

Front

What type of reasoning is based on facts and accepted properties?

Back

Deductive reasoning is based on facts, definitions, accepted properties, and the laws of logic.

Front

What is the law of syllogism?

Back

The law of syllogism states that if 'p → q' and 'q → r' are true, then 'p → r' is also true.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'p → q' is '~q → ~p'. It negates both the conclusion and the hypothesis and reverses them.

Front

What is an example of a conditional statement?

Back

An example of a conditional statement is 'If it rains, then the ground will be wet.'

Front

What is the converse of a conditional statement?

Back

The converse of a conditional statement 'p → q' is 'q → p'. It reverses the hypothesis and conclusion.

Front

What is the next term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ...?

Back

The next term is 13, as each term is the sum of the two preceding terms.

Front

What is the definition of a conditional statement?

Back

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

Front

What does it mean to negate a statement?

Back

To negate a statement means to state that the statement is not true, often represented by the symbol '~'.