Please see the attached document for the questions I need help with for a review it is discrete mathematics. 

 

 

1. Mark each of the following as true or false.
{a, b, c} ⊂ {a, b, {c}}
c ⊂ {c}
c ∈ {c}
∅ ∈ {c}
∅ ⊂ {c}
2. One of the sets listed below is a subset of another. Which is a subset of which?
A = {n : n is a prime integer and n > 2}
B = {n : n is an integer and 1 ≤ n ≤ 20}
C = {1, 3, 5, 7, 9, . . .}
3. Find the power set of {7, 11, 13}.
4. Given the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and given
A = {1, 3, 7, 8, 9}
B = {2, 3, 6, 7, 10}
C = {1, 5, 6, 8}
list the elements in the following sets.
•A∩C
• B’
• A’ ∩ B’
5. Prove that if A, B, C are any sets, then A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
6. Given the sets
A = {n : : n = 4u for some positive integer u}
B = {n : : n = 3v + 1 for some positive integer v}
list the six smallest elements of A ∩ B. 3
7. Construct a truth table for ∼p ∨ ∼(q ∧ ∼r).
8. Show that the statement is a tautology. ((p ↔ q) ∧ ∼p) → ∼q 4
9. Show that the statement is a tautology. (p ∧ q) → (p ∨ ∼q)
10. Show that the statement is a contradiction. p ∧ (q ∧ ∼p) 5
11. Prove the following. (p → q) ≡ (∼p ∨ q)
12. Determine whether the following is a valid argument. (p → ∼q), (∼r → p), q ` r 6 13. Translate the following argument into symbols. Is it a valid argument?
Premise 1: A dog does not bark a lot if and only if he is friendly.
Premise 2: A chihuahua barks a lot.
Premise 3: My dog is friendly.
Conclusion: My dog is not a chihuahua. 14. Express each of the following using predicates and quantifiers.
• All people who are comedians are funny.
• All people are comedians and are funny.
• Some people who are comedians are funny.
• Some people who are comedians are not funny

Attachments:

• 1492568422-MADT1Review.docx