2. Write the converse, inverse and contrapositive of: "If we have a quiz today, then we will not have a quiz tomorrow.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.3: Preparing To Do Analytic Proofs
Problem 31E
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1. Write each of the following in "If p, then q" form.
a. Every square is a rectangle.
b. Being older than 30 is sufficient to show that I am at least 21.
2. Write the converse, inverse and contrapositive of: "If we have a quiz today, then we will not have
a quiz tomorrow.
3. Determine whether the given statements are equivalent.
a. If a = b, then a · c = b.c
If a + b, then a · c + b ·c
b. If I live in Nashville, then I live in Tennessee.
If I do not live in Tennessee, then I do not live in Nashville.
4. Write the contrapositive of each statement and use he contrapositive to determine whether the
original statement is true or false.
a. If 3 + x is an odd integer, then x is an even integer. (Assume x is an integer)
b. If two triangles are not similar triangles, then they are not congruent triangles.
Note: Similar triangles have the same shape. Congruent triangles have the same size and
shape.
c. If today is not Wednesday, then tomorrow is not Thursday.
Transcribed Image Text:1. Write each of the following in "If p, then q" form. a. Every square is a rectangle. b. Being older than 30 is sufficient to show that I am at least 21. 2. Write the converse, inverse and contrapositive of: "If we have a quiz today, then we will not have a quiz tomorrow. 3. Determine whether the given statements are equivalent. a. If a = b, then a · c = b.c If a + b, then a · c + b ·c b. If I live in Nashville, then I live in Tennessee. If I do not live in Tennessee, then I do not live in Nashville. 4. Write the contrapositive of each statement and use he contrapositive to determine whether the original statement is true or false. a. If 3 + x is an odd integer, then x is an even integer. (Assume x is an integer) b. If two triangles are not similar triangles, then they are not congruent triangles. Note: Similar triangles have the same shape. Congruent triangles have the same size and shape. c. If today is not Wednesday, then tomorrow is not Thursday.
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