Chapter 2-2
Logic Boy continues to help Point Man with this chapter by creating this notes page for conditional statements – what he likes to call if, then statements. This section is the beginning of doing proofs in which you use if, then statements to logically follow a line of thinking while proving a theorem. Point Man needs you to understand these tables in order to increase your ability to speak Geometry.
Point Man has drawn two tables below that he would like you to use the classroom set of books to fill. These two tables will be used in the practice problems.
Conditional Statements
Definitions / Symbols / Venn DiagramA conditional statement is a statement that can be written in the form, “If p, then q”. / p q /
The hypothesis is the part p of a conditional statement following the word if.
The conclusion is the part q of a conditional statement following the word then.
Related Conditionals
Definitions / SymbolsA conditional is a statement that can be written in the form, “If p, then q”. / p q
Converse:
The converse is the statement formed by exchanging the hypothesis and conclusion / q p
Inverse:
The inverse is the statement formed by negating the hypothesis and conclusion / ~p ~q
Contrapositive:
The contrapositive is the statement formed by both exchanging and negating the hypothesis and conclusion / ~q ~p
Point Man has one definition he wants you to know, so define it below.
1. Negation – of p is “not p”, written ~p, of q is “not q”, written ~q. The negation of a false statement is true and the negation of a true statement is false.
Underline the hypothesis once and the twice in each conditional statement.
1. If you eat breakfast, then you will feel better at school.
2. If two lines are perpendicular, then they form right angles.
3. If two angles are supplementary, then their sum is 180°.
4. If a nonzero number has exactly two factors, then the number is prime. Write each statement in if-then form.
5. All students at Hermitage take an English class.
6. All right angles measure 90°.
7. Every dog has four legs. 8. All vertical angles are congruent.
9. All cats chase mice.
Write the converse, inverse, and contrapositive of each conditional statement.
10. If it is Saturday, then school is closed.
Converse:______.
Inverse:______.
Contrapositive:______.
11. If two angles are complementary, then they total 90°.
Converse:______.
Inverse:______.
Contrapositive:______.
12. If a line bisects a segment, then the segment is divided into two congruent parts.
Converse:______.
Inverse:______.
Contrapositive:______.
13. If it rains, then I will not go.
Converse:______.
Inverse:______.
Contrapositive:______.
14. If two angles form a linear pair, then they are supplementary.
Converse:______.
Inverse:______.
Contrapositive:______.
Let p represent “Daniel is angry”, and let q represent “Daniel is not having fun”.
Translate the following into symbolic form.
15. Daniel is not angry. ______
16. Daniel is angry and Daniel is not having fun. ______
17. Daniel is not angry or Daniel is not having fun. ______
Translate the following from symbolic form to written form.
18. p ~ q ______.
19. ~ q p ______.