Master Determine the Truth of conditional statements and which ones are logically equivalent

The video tutorial explains how to determine the truth of conditional statements, including their converse, inverse, and contrapositive. It discusses logical equivalence and provides examples using geometric shapes like squares and polygons. The tutorial emphasizes understanding the logical relationships between different forms of statements and their truth values.

What is the contrapositive of a conditional statement?

• The opposite of the conclusion and hypothesis

• The opposite of the hypothesis and conclusion

• Swapping the hypothesis and conclusion

• Swapping the conclusion and negating the hypothesis

Why is the statement 'If you have 4 equal sides, then you have a square' false?

• A triangle can have 4 equal sides

• A square can have unequal sides

• A rhombus has 4 equal sides but is not a square

• A rectangle has 4 equal sides but is not a square

Which statements are logically equivalent?

• Converse and contrapositive

• Conditional and inverse

• Conditional and contrapositive

• Inverse and contrapositive

What makes a polygon regular?

• Having unequal side lengths and equal angle measurements

• Being a closed 2-dimensional figure with unequal angles

• Having equal side lengths and equal angle measurements

• Being a closed 3-dimensional figure

What is the inverse of the statement 'If you have a polygon, then it is a regular polygon'?

• If you have a polygon, then it is not a regular polygon

• If you have a regular polygon, then it is a polygon

• If you do not have a regular polygon, then it is not a polygon

• If you do not have a polygon, then it is not a regular polygon

Why is the contrapositive of 'If you have a polygon, then it is a regular polygon' false?

• A rectangle is not regular but is a polygon

• A square is not regular but is a polygon

• A triangle is not regular but is a polygon

• A circle is not regular but is a polygon

What does it mean for two statements to be logically equivalent?

• They have the same negation

• They have the same conclusion

• They have the same hypothesis

• They have the same truth value