Math TEST

MAT-130 Test 2 Spring 2021 Name:_________________________________ This is a Take-Home test; please read the instructions in the provided document. Please show work except for problems 1-13. Decide whether each statement is true or false. (2 points each)

1. Given that 𝑝 is false and ¬𝑞 is true, the conditional ¬𝑝 → 𝑞 is false. 2. Base 15 needs 14 distinct symbols.

3. In base nine the greatest five digit number is 88888!.

4. A statement is not a declarative sentence.

5. The sentence “Yesterday John went to Hoboken” is not a compound statement.

6. The negation of “I will go to Caldwell or I will go to Austin” is “I will not go to Caldwell or I will not go

to Austin”. 7. The negation of “It is not easy or I am lazy” is “It is easy and I am lazy”.

8. The sentence “This is a fast mouse” is a compound statement.

Decide whether each of the following is a statement or not. (2 points each)

9. 21 − 25 ≠ −6.

10. This website is not very interesting.

11. I shall buy a car or my sister goes running with her best friend.

Write a negation of the following. Make sure that your answer is also an inequality. (3 points each)

12. 𝑥 + 28 > −100

13. 𝑥 ≤ 345

Assume p is true, q is false, and r is false. Find the truth value of the following statements. (6 points each) 14. (¬𝑞 ∧ 𝑟) → ¬𝑟 15. (𝑝 ∧ 𝑞) → ¬𝑞

Construct a truth table for the following compound statement and state if it is a tautology. (7 points) 16. (¬𝑝 ∧ 𝑞) → 𝑞 Construct a truth table to determine whether the argument is valid or invalid. (8 points)

17. 𝑝 → 𝑞 𝑞 ∧ 𝑝 _________ 𝑞 ∨ 𝑝 Convert each number to decimal form (base ten). (6 points each) 18. 310400! 19. 𝐴𝐴𝐴0!" 20. 12345! Convert each number from decimal form (base ten) to the given base. (7 points each) 21. 480 to base two. 22. 43775 to base sixteen. 23. 3120 to base five. Convert the following number to the given base. 24. 34445! to base seven. (6 points)