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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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ANSWER #3

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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