Search & Filtering
Let A = {2, 3, 5, 7, 11, 13} and B = {A, 2, 11, 18}.
1. Find A ∪ B. 2. Find A ∩ B. 3. Find A − B.
Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply
a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)
1. Let p and q be the propositions “Swimming at the Corregidor Island shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence.
Three persons enter into car, where there are 5 seats. In how many ways can
they take up their seats?
There are four roads from city X to Y and five roads from city Y to Z, find
(i) how many ways is it possible to travel from city X to city Z via city Y.
(ii) how different round trip routes are there from city X to Y to Z to Y and back
to X.
Teams A and B play in a tournament. The first team to win three games wins the
tournament. Find the number n of possible ways the tournament can occur.
Mark and Erik are to play a tennis tournament. The first person to win two
games in a row or who wins a total of three games wins the tournament. Find
the number of ways the tournament can occur.
Two Balls are to be selected without replacement from a bag that contains one
red, one blue, one green and one orange ball. A) Use the counting principle to
determine the number of possible points in the sample space. Construct a tree
diagram and list the sample space.
Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses.
Find the number N of students in a dormitory given the data:
12 take A, 5 takeAand B, 4 takeB and D, 2 take B, C,D,
20 take B, 7 takeAand C, 3 takeC and D, 3 take A, C,D,
20 take C, 4 takeAand D, 3 take A, B,C, 2 take all four,
8 take D, 16 takeB and C, 2 take A, B, D, 71 take none.
Suppose among 32 people who save paper or bottles (or both) for recycling,
there are 30 who save paper and 14 who save bottles. Find the number m of
people who:
(a) save both; (b) save only paper; (c) save only bottles.
