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A timing diagram is given for inputs to a basic D Flip-Flop. What is the value of the Q output of the D Flip-Flop at time = 7 ns? Assume the delay from inputs changing to output changing is negligible.

Q1-8 points Use truth tables (only) to verify logical equivalence    

Q5-5 points Consider the statement “The square of any odd integer is odd.” Write a negation for the statement.

Q8-10 points Use mathematical induction to prove that, for every integer

Q7-7 points Prove the following statement directly or disprove it by counterexample, stating your conclusion as True or False:

Q5-5 points Consider the statement “The square of any odd integer is odd.” Rewrite the statement in the form ∀ _____ n, if ____ then ____ . (Make sure you use the variable n when you fill in each of the second two blanks.)

Q5-5 points Consider the statement “The square of any odd integer is odd.” Rewrite the statement in the form ∀____ n, ____ . (Do not use the words “if” or “then.”)

Q2-10 points Write the following two statements in logical form and use truth tables (only) to determine whether they are logically equivalent. Statement 1: If Sam bought it at Crown Books, then Sam didn’t pay full price. Statement 2: Sam bought it at Crown Books or Sam paid full price.

Q6- 8 points Write a proof for the following statement: For all sets A and B, if A ⊆ B, then A ∪ B = B.

Q12 – 6 points Draw a Venn diagram for sets A, B and C satisfying the following conditions: A ⊆ C, B ⊆ C, A ∩ B = ∅.