Unformatted text preview: 71'r2. (0) False, because the hypothesis of this implicatio~ is true, but the conclusion is false. (p) [BB] This is true: The hypothesis is true only when a ~ band b ~ a, that is, when a = b, and then the conclusion is also true. (q) This implication is true because the hypothesis is always false. 1 3. (a) [BB] If x > 0, then -> O. x (b) If a and b are rational numbers, then ab is a rational number. (c) If f is a differentiable function, then f is conti~uous. (d) [BB] If 9 is a graph, then the sum of the degrees of the vertices of 9 is even. (e) [BB] If A is a matrix and A # 0, then A is invertible. (f) If P is a parallelogram, then the diagonals of P bisect each other. (g) If n is an even integer, then n < O. (h) If two vectors are orthogonal, then their dot product is O. (i) If n is an integer, then n~l is not an integer. (j) If nis a natural number, then n + 3> 2. 4. (a) [BB] True (the hypothesis is false). (b) True (hypothesis and conclusion are both true). 1...
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- Summer '10
- Graph Theory, Prime number, Rational number