Quiz 1 answer key
Math 1030-005 (Fall 2014)
1. Solve for x: 4x − 2 = 3 − 5x. (3 points)
Sol. 4x + 5x = 3 + 2, x = 5/9.
2. Evaluate:
2
3
× 14 + 16 ÷ 51 . (3 points)
Sol. It equals 1/6 + 5/6 = 1.
3. Venn diagram: (3 points)
(1) How many women are at the party? Sol. (1)7 + 4 = 11.
(2) How many people are at the party? Sol. (2)3 + 5 + 4 + 7 = 19.
4. Consider the following deductive arguments: (everyone gets 3 points)
(Premise 1) If someone lives in Colorado, he/she live in Denver.
(Premise 2) Tom does not live in Colorado.
(Conclusion) Tom does not live in Denver.
(a) Is this argument valid? (which means the conclusion follows from all the premises)
Sol. Invalid, for we may find someone who does not live in Colorado but live in Denver. - but this
is not true in real life, which is confusing to many students. Since I think this problem is not properly
designed, I decide to give full points to everyone. But always keep in mind that when we judge a argument is valid or not, we always assume all the premises are true, as you can also see in the textbook.
(b) Draw a small circle “live in Colorado”, and a larger one containing it, called “live in Denver”.
Mark a cross sign on an appropriate place for Tom, to show why your answer for (a) is valid or invalid.
Sol. You should mark the cross sign somewhere between the smaller circle and the larger one, or
on the larger one.