Write the following two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words explaining how the truth table supports your answer.
If Sam bought it at Crown Books, then Sam didn’t pay full price.
Sam bought it at Crown Books or Sam paid full price.
Solution 1: The given statements are not logically equivalent. Let p be “Sam bought it at Crown
Books,” and q be “Sam didn’t pay full price.” Then the two statements have the following form:
p ? q and p? ? q:
The truth tables for these statement forms are
Rows 2 and 3 of the table show that p ? q and p? ? q do not always have the same truth values, and
so p ? q ?? p? ? q:
Solution 2 : The given statements are not logically equivalent. Let p be “Sam bought it at Crown
Books,” and q be “Sam paid full price.” Then the two statements have the following form:
p ?? q and p ? q:
The truth tables for these statement forms are
Rows 1 and 4 of the table show that p ?? q and p ? q do not always have the same truth values, and so p ?? q ?? p ? q:
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A. Valid B. Invalid
Solve the system of equations.x + 5y + 5z = -8 4y + 5z = -3 z = 1
A. x = -3, y = 1, z = -2 B. x = -3, y = -2, z = 1 C. x = 1, y = -2, z = -3 D. Inconsistent
Match the polynomial function with the graph.y = -x4 + 4x2
A. 
B. 
C. 
D. 
Use the graph to estimate any solutions to the given equation on the interval 
tan x = tan2 x
A. 
, 
B. 0, 
, ? , 
C. None
D. 0, ?