Decide whether the statement makes sense. Explain your reasoning.The propositions "I am hungry" and "I am not hungry" are both true, since sometimes I am hungry and sometimes I am not hungry.
What will be an ideal response?
Does not make sense. The second proposition is the negation of the first proposition. If a proposition is true, then its negation must be false, and vice versa. Thus, the two propositions cannot both be true. But, you argue, I was hungry at 7:00 this morning, but then I ate breakfast and I was not hungry at 8:00. The explanation is that "I was hungry at 7:00 this morning" and "I was hungry at 8:00 this morning" are two different propositions. The first one is true and its negation is false, while the second one is false and its negation is true. (Explanations will vary.)
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Simplify the complex fraction.
A. 
B. 
C. 45y(y + 8)
D. 
Simplify.
A. 
B. 
C. - 
D. 
Solve the equation. If the equation is an identity or a contradiction, state this.3(x - 1) + x = 4(x + 1) - 7
A. ? or { }; contradiction B. {0} C. {3} D. all real numbers; identity
Let v and w be two vectors in the plane with given magnitudes. The angle between v and w is ?. Find the expression. Round the answer to the nearest tenth.
= 7, 
= 12, ? = 74°
Find the angle between v - w and v
A. 33.8° B. 25.7° C. 48.1° D. 72.4°