DS1 FINAL EXAM REVIEWER

If a relation R on a set A is symmetric, which of the following must be true?

• For all a,b∈A, if aRb, then aRb holds.

• For all a,b ∈ A, if aRb then bRa

• For all a ∈ A, aRa

• For all a,b, c ∈ A, if aRb and bRc, then aRc

How many different 5-letter words can be formed using the letters A, B, and C with repetition allowed?

• 150

• 120

• 125

• 243

Answer explanation

3^5 = 243

In how many ways can you select 3 out of 8 distinct objects?

• 336

• 56

• 112

• 672

Which of the following relations on R (the set of all real numbers) is an equivalence relation?

• {(x,y)∣x≠y}

• {(x,y)∣x=y}

• {(x,y)∣x≥y}

• {(x,y)∣x≤y}

Answer explanation

Equivalence relation means that x and y are the same values, thus it should be x=y.

If you flip a coin 3 times, how many possible outcomes are there?

• 16

• 4

• 6

• 8

If you have 5 different hats and you want to choose 2 to wear in a specific order, how many ways can you do this?

• 30

• 25

• 20

• 10

In a network of computers, each computer is a node and each direct connection between computers is an edge. The number of direct connections a computer has is referred to as what in graph terminology?

• Adjacency

• Path

• Loop

• Degree

Answer explanation

"direct connections" refer to the end-to-end points of the computer, which is also equivalent to degrees in graphs.

How many ways can you arrange 3 distinct books on a shelf?

• 9

• 6

• 12

• 3

In the set {a,b,c}, which of the following is a symmetric relation?

• {(a,b)}

• {(a,b),(b,a),(b,c),(c,b)}

• {(a,a),(b,b),(c,a)}

• {(a,c),(b,a),(c,b)}

Answer explanation

Symmetric relation refers to elements having a "partner pair", meaning if theres (a,b) then there exists (b,a)

In a classroom of 10 students, how many ways can you choose a president and a vice-president?

• 100

• 20

• 90

• 45