1. If A = {a,b,c} and B = { 1, 2 } then how many relations with 3 tuples are pos
ID: 3740169 • Letter: 1
Question
1. If A = {a,b,c} and B = { 1, 2 } then how many relations with 3 tuples are possible using the Cartesian product A x B
a.6C6
b.6C3
c.16C3
d.None of the above
2. If A = {a,b,c} the Power set P (A) contains the following
a.{ {}, {a}, {b}, {c}, {a,c}, {a,b} {b,c}, {a,b,c} }
b.{ {a}, {b}, {c}, {a,c}, {a,b} {b,c}, {a,b,c} }
c.{ {a,b,c} }
d.None of the above
What is the Cartesian product of A = {1, 2} and B = {a, b}?
a{ (1, a), (1, b), (2, a), (b, b) }
b { (1, 1), (2, 2), (a, a), (b, b) }
c { (1, a), (2, a), (1, b), (2, b) }
d { (1, 1), (a, a), (2, a), (1, b)}
(+5) Given the following sets A = {1, 2, 3} and B = {a, b}, which of the following are functions given the Cartesian product A x B?
a { (1, a), (2, b), (3,b) }
b { (1, a), (2, a), (3, a) }
c { (1, a), (2, a), (1, b), (3, a) }
d None of these
a, b c B. a, b C. b D. b c D. d
(+5) In a hash table of size 13 which index positions, using the hash function h(key) = key % 13 would the following two keys map to ? 27, 130
a 1, 12
b 12, 0
c 1, 0
d none one these
(+5) Which formula would you use to pick a team of 3 people from a group of 10
a. 10C3 b. 10p3 c. 7c3 d.7p3 e. none
(+5) Which formula would you use to pick a President, VP and mascot from a group of 10
a.10c3 b. 10p3 c. 7c3 d. 7p3 e.none
Explanation / Answer
1. If A = {a,b,c} and B = { 1, 2 } then how many relations with 3 tuples are possible using the Cartesian product A x B
Answer: Option b.6C3
Explanation: Cartesian product of A = {a,b,c} and B = { 1, 2 } is { (a, 1), (a, 2), (b,1), (b,2), (c,1), (c,2) }
2. If A = {a,b,c} the Power set P (A) contains the following
Answer: Option a.{ {}, {a}, {b}, {c}, {a,c}, {a,b} {b,c}, {a,b,c} }
3) What is the Cartesian product of A = {1, 2} and B = {a, b}?
Answer: Option c { (1, a), (2, a), (1, b), (2, b) }
4) Given the following sets A = {1, 2, 3} and B = {a, b}, which of the following are functions given the Cartesian product A x B?
a { (1, a), (2, b), (3,b) }
b { (1, a), (2, a), (3, a) }
c { (1, a), (2, a), (1, b), (3, a) }
d None of these
Answer: Option D. d
5) Which formula would you use to pick a team of 3 people from a group of 10
Answer: Option a. 10C3
Explanation: In Combination: Picking a team of 3 people from a group of 10.
C(10,3) = 10!/(7! · 3!) = 10 · 9 · 8 / (3 · 2 · 1) = 120.
6) Which formula would you use to pick a President, VP and mascot from a group of 10
Answer: Option b. 10p3
Explanation: In Permutation: Picking a President, VP and Waterboy from a group of 10.
P(10,3) = 10!/7! = 10 · 9 · 8 = 720.
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