(1) If A is an uncountable (2) Z† × Z is a countable set. Select one of the following choices: set and B is a countable set, then A - B can be a countable set. (a) (1) is True and (2) is False. (c) (1) and (2) are True. (b) (1) is False and (2) is True. (d) (1) and (2) are False.

Let p and q represent the following statements. p: The test is not today. q: There are not nine notes in a major scale. Express the following statement symbolically. There are nine notes in a major scale. ..... The statement written symbolically is

Write the following statement using the words "if ... then." "To graduate this semester, it is sufficient that you have completed 18 credits. " The statement equivalently written using the words "if . then" is which of the following? A. If you have not completed 18 credits, then you graduate this semester B. If you graduate this semester, then you have completed 18 credits. OC. If you do not graduate this semester, then you have completed 18 credits. O D. If you have completed 18 credits, then you graduate this semester.

I need #11 and #13 DIRECTIONS: For each proof, you must include (i.e., write) the premises in that proof. I do not want to see any proofs without premises. Do not use any transformation rules (e.g. contraposition) in your proof other than DN. Only use the eight inference rules. YOU CANNOT USE CONDITIONAL PROOF (CP), INDIRECT PROOF (IP), OR ASSUMED PREMISES (AP). You will lose points if you use any of the inference rules Resolution, Contradiction, Transposition,