midterm-sample - MACM 101 Midterm Test This is a sample...

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Unformatted text preview: MACM 101 Midterm Test This is a sample! Some Day, 2007 First Name and Initials Last Name Student No. NO AIDS allowed. Answer ALL questions on the test paper. Use backs of sheets for scratch work. Total Marks: 100 1. State DeMorgan’s law [8] 2. Show that ¬(p → q) → ¬q is a tautology. [12] 3. Show that (p → q) → r and p → (q → r) are not logically equivalent. [16] 4. Give the reasons for each step needed to show that the following argument is valid Premises: p, p → q, s ∨ r, r → ¬q Conclusion: s. [16] Steps 1. p 2. p → q 3. q 4. r → ¬q 5. q → ¬r 6. ¬r 7. s ∨ r 8. s Reasons 5. How to prove that a universally quantified statement is false? [12] 6. Show that ∃x (P (x) ∨ Q(x)) is not logically equivalent to (∃x P (x)) ∨ (∃x Q(x)). [16] 7. What is the power set? [12] 8. What is a 5-ary relation? [8] ...
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