Math
Let A={2,3,5} B={0,3,7}find A∪B
A∪B = { 0, 2, 3, 5, 7 }
Let A = {x, y, z} B = {a, b, c} find |A x B|
| means elements | A x B = { x, y, z } x { a, b, c } A x B = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c) (z, a), (z, b), (z,c)} 9 elements
Given set A={5,r,#,y}find |P(A)|
|P(A)| = ø, {5}, {r}, {#}, {y}, {5, r, #,y}, {5, r}, {5, #}, {5,y}, {r, #}, {r, y}, {#, y} or 24 = 16 since there are 4 elements. 16 elements
Given sets A and B, where|A|=12,|B|=13,and|A∪B|=20 Find|A⊕B|
12+13=25 elements total Elements in the Union = 20 25-20 = 5 (the difference and elements in the intersection, so remove 5 elements from the union) |A⊕B| = 15
A combination lock uses 3 numbers from 0-49. How many possible combinations exist? (Numbers can be repeated)
125000
How many ways can 8 students be seated in a class with 15 desks?
15P8 or 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 = 259,459,200 different ways
A flush in a five-card poker hand is five cards of the same suit. The suits are spades, clubs, diamonds and hearts. How many flushes are possible in any suit?
4 x 13C5 = 5148 possible flushes
Let A = {1, 2} B = {a, b, c}find A x B
A x B = { 1, 2 ) x { a, b, c } A x B = { (1, a), (1, b), (1, c), (2, a), (2, b), (2, c) }
Let A={1,2,3} B={p,q}find A^2
A2= {1, 2, 3} x {1, 2 ,3} A2= {(1,1),(1,2)(1,3),(2,1),(2,2), (2,3), (3,1),(3,2),(3,3)}
Let A = {4, 5, 8} B = {3, 8, 7} find A∩BLet A = 4, 5, 8 B = 3, 8, 7 find A∩B
A∩B = { 8 }
How many ways can 3 boys and 2 girls line up so that no two boys are next to each other?
(3!)(2!) = 12
A jar contains 8 marbles numbered 2-9. How many ways can 1 prime and 1 composite number be selected regardless of order?
(4 / 1)(4 / 1)=16 combinations
As a freshman, suppose you had to take two of four lab science courses, one of two literature courses, two of three math courses, and one of seven physical education courses. Disregarding possible time conflicts, how many different schedules do you have to choose from? (order is not relevant)
(4/ 2)(2 / 1)(3 / 2)(7 / 1)=252 ( combinations )
How any ways can I select a set of two distinct prime numbers less than 20?
(8!/ 2!)=28
Let A={3,4,5} B={3,5} C={4,5}find (A∩C)∩B Let A={3,4,5} B={3,5} C={4,5}find (A∩C)∩B
The intersection between all three equals: {5}
Suppose that a single character is stored in a computer using eight bits. How many bit patterns have exactly 4 zeros?
When finding the number of zeros in the bit pattern, this would invoke combinations, which would look like this: 8C4. This means 8 (the number of bits) Choose 4 (which is the exact number of zeros patterns). 8C4 or 8!/4!4! = 70 bit patterns have exactly 4 zeros.
List the elements of {2n+1 | n=1,2,3,4}
input all numbers in for "n"