Logic ReviewName______
Use the following conditional statement to answer the problems: “If I win, then you don’t lose.”
1. Write the hypothesis. ___I win______
2. Write the conclusion. ___You don’t lose______
3. Negate the hypothesis. __I don’t win______
4. Negate the conclusion. ___You lose______
5. Write the converse. __If you don’t lose, then I win______
6. Write the inverse. ____If I don’t win, then you lose______
7. Write the contrapositive. _If you lose, then I don’t win______
8. Write the bi-conditional. __I win if and only if you don’t lose______
9. Write each of the following statements in symbolic notation.
Let p: you see lightning q: you hear thunder.
a. If you see lightning, then you hear thunder. __p → q______
b. If you hear thunder, then you see lightning. __q → p______
c. If you don’t see lightning, then you don’t hear thunder. ___~p → ~q______
d. If you don’t hear thunder, then you don’t see lightning. ___~q → ~p______
10. Statement 1: “If two adjacent angles form a linear pair, then the sum of the measures of the angles is 180°.”
Statement 2: “If the sum of the measures of two angles is 180°, then the angles are supplementary.”
By the Law of Syllogism, which statement below follows from Statements 1 and 2?
a. If the sum of the measures of two angles is 180°, then the angles form a linear pair.
b. If two adjacent angles form a linear pair, then the sum of the measures of the angles is 180°.
c. If two adjacent angles form a linear pair, then the angles are supplementary.
d. If two angles are supplementary, then the sum of the measures of the angles is 180°.
11. Buzzwords. Write the action you are supposed to take in order to create each sentence.
Converse__switch______Inverse__negate______Contrapositive__switch and negate___
12. p = a shape is a square q = a shape has all congruent sides
Write in words
a. p→ q _If a shape is a square, then it has all congruent sides______
Truth value: __True______Counterexample: ______
b. ~p→ q _If a shape is not a square, then it has all congruent sides______
Truth value: __False______Counterexample: _Rectangle______
c. q→ p __If a shape has all congruent sides, then it is a square______
Truth value: __False______Counterexample: __Equilateral Triangle______
d. ~p→ ~q __If a shape is not a square, then it does not hall all congruent sides______
Truth value: __False______Counterexample: __Equilateral Triangle______
13. Determine if the bi-conditional statement is true.
“A triangle is isosceles if and only if the triangle has two congruent (equal) sides.”
Write the conditional: If a triangle is isosceles, then it has two congruent sides True or False? _True___
Write the converse: If a triangle has two congruent sides, then it is isosceles_ True or False? _True____
Is the bi-conditional statement true or false? _True______
14. Determine if the bi-conditional statement is true.
“An angle is an acute angle if and only if its measure is 45°.”
Write the conditional: _If an angle is acute, then it measures 45°______
______True or False? _False__
Write the converse: _If an angle measures 45°, then it is acute______
______True or False? _True___
Is the bi-conditional statement true or false? __False______
15. Use the Law of Syllogism to place the following statements in order (just use the letters).
W: If the cold front comes in, then it will get below 20°
X: If it snows today, then I will wear my gloves.
Y: If I wear my gloves, my fingers will get itchy.
Z: If it gets below 20°, then it will snow today.__W______Z__ ___X__ __Y___