MTH 314 Midterm: MTH314 - F2002 Midterm Solutions
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Mth 314 midterm solutions p q r p q (p q) r q r p (q r) The columns for (p q) r and p (q r) are identical, so these statement forms are equivalent. r s. 10: q w (10; disjunctive addition) (4, 5; dysjunctive syllogism) (3, 6; modus ponens) (1, 7; modus ponens) (8; conjunctive simpli cation) (2, 9; modus tollens) u. 3. (a) x r, x t x i (b) x t, x i (c) x t s. t. x 6 i or. X r s. t. x t x 6 i. The bell does not toll, but the clock strikes. 5. (a) i, ii, iii, i , ii (b) n, n, y, n (note: 1 mark deducted for every wrong answer in part (b), min on part (b) is 0: let x z, with 4 | x. Thus there exists k z, such that x = 4k (de nition of divisibility )
