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Learning Task 3 A. Prove the following using Direct Proof 1. Given: Odd and even integers Prove: the sum of odd and even integers is odd integer Solution: Supply the missing statement and reason Statement Reason 1. Let x be odd integer and y A variable represents a number even integer 2. x = 2k + 1 3. y = 2k 4. x + y = (2k + 1) + 2k Adding two integers (from statement 1 and 2) 5. x + y = 2(2k) + 1 6. x + y = 2r + 1 r = 2k, substituting r to 2k in statement 5 2. Given odd integer m and even integer n ( m = 2k + 1 and n = 2k) Prove: mn is even number ( mn = 2r) 3. Given: n is even number (n = 2k) Prove: 3n + 5 is an odd number. ( 3n + 5 = 2m + 1) B. Prove the following using indirect proof. 1. If x = 3, then 3x + 5 # 10. 2. If a triangle is an isosceles triangle ( 2 sides are equal), then the base angles cannot measure 92 degrees. 3. Given: 3r - 5 # 13 Prove: r # 6 4. Given: x = 5 Prove : 2x + 4 # 12