Discrete Math Question

Section 1: Logic

1. If p = true and q = false, find the truth value of:

p land q

Answer: False

2. What is the negation of:

It is sunny and warm.

Answer: It is not sunny OR not warm.

3. Complete the statement:

If p rightarrow q is false, what must be true?

Answer:

p is true and q is false.

Section 2: Sets

Let

A = {1, 2, 3}

B = {3, 4, 5}

4. Find A cup B

Answer: {1,2,3,4,5}

5. Find A cap B

Answer: {3}

6. How many elements are in the power set of A?

Answer: 2^3 = 8

Section 3: Even & Odd Reasoning

7. Is this statement true or false?

The sum of two odd numbers is odd.

Answer: False

Example: 3 + 5 = 8 (even)

8. An even number can be written as ___.

Answer: 2n (where n is an integer)

Section 4: Counting & Combinatorics

9. How many ways can you arrange the letters in CAT?

Answer:

3! = 6

10. How many different 2-digit numbers can be made using digits 1, 2, 3 without repetition?

Answer:

3 choices for first digit

2 choices for second

3 2 = 6

11. In how many ways can 4 students sit in a row?

Answer:

4! = 24

Section 5: Relations & Functions

12. On the set {1,2,3}, does the relation

R = {(1,1), (2,2), (3,3)}

have the reflexive property?

Answer: Yes

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