SCCS Geometry Logic Practice

Front

What is an inverse statement in logic?

Back

An inverse statement is formed by negating both the hypothesis and the conclusion of a conditional statement. For example, the inverse of 'If P, then Q' is 'If not P, then not Q.'

Front

What does it mean when a conclusion states 'Not all automobiles are motorized vehicles'?

Back

This conclusion suggests that there exists at least one automobile that is not a motorized vehicle, which contradicts the definition of motorized vehicles.

Front

What can be concluded from the statements: 'If Tom goes fishing then he brings a pole' and 'If Tom brings his pole then he catches a fish'?

Back

It can be concluded that 'If Tom goes fishing, then he catches a fish' through the transitive property of implications.

Front

How do you write a conclusion from the statement: 'If it is Friday then I will get paid'?

Back

The conclusion is 'I will get paid' if the condition 'it is Friday' is true.

Front

What is the converse of the statement: 'If you make an insurance claim, then your rates will go up'?

Back

The converse is 'If your insurance rates go up, then you have made an insurance claim.'

Front

Define a conditional statement in logic.

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, typically in the form 'If P, then Q'.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' It is logically equivalent to the original statement.

Front

Explain the difference between a hypothesis and a conclusion in a conditional statement.

Back

The hypothesis is the 'if' part of the statement, while the conclusion is the 'then' part. For example, in 'If it rains, then the ground is wet,' 'it rains' is the hypothesis and 'the ground is wet' is the conclusion.

Front

What is a valid conclusion in logical reasoning?

Back

A valid conclusion is one that logically follows from the premises or statements provided, based on the rules of logic.

Front

What does it mean for a statement to be logically equivalent?

Back

Two statements are logically equivalent if they have the same truth value in every possible scenario.