Mastering Reasoning and Proofs

Front

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

Back

Deductive reasoning.

Front

If a polygon is a quadrilateral, then it is a trapezoid. What is the contrapositive of this statement?

Back

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

Front

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2).

Back

y = -1/3x + 1.

Front

Use the Law of Syllogism: If soccer practice is cancelled, then you can go to the mall after school. If it is raining today, then soccer practice is cancelled. Write a new conditional statement.

Back

If it is raining today, then you can go to the mall after school.

Front

What is the correct equation to solve for X? 16X + 180 = 90, 12X - 19 = 4X + 1, 12X - 19 + 4X + 1 = 90, 12X - 19 + 4X + 1 = 180

Back

12X - 19 + 4X + 1 = 180.

Front

What is the definition of deductive reasoning?

Back

Deductive reasoning is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.

Front

What is the Law of Syllogism?

Back

The Law of Syllogism states that if 'p implies q' and 'q implies r', then 'p implies r'.

Front

What is a contrapositive in logic?

Back

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

Front

What is the slope of a line perpendicular to a line with a slope of 3?

Back

The slope of a line perpendicular to a line with a slope of 3 is -1/3.

Front

What is the formula for the slope-intercept form of a line?

Back

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.