Use proof by contradiction to prove the statement below: If s t Z ,  and s  2 , then s | t or s | (t +1) . Note: (i) 2

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Use proof by contradiction to prove the statement below: If s tZ ,  and s  2 , then s | t or s | (t +1) . Note: (i) 2 | 4denotes 2 divides 4 and 2| 3 denotes 2 does not divide 3. (ii)Definition of divisibility, a b| if an only if ac b = where a b, and c +  . (iii) By De Morgan’s Law, the negation of “ s | t or s| (t +1) ” is “ st| and s t | 1 ( + ) ”.
(c) Use proof by contrapositive to prove the statement below:Let x . If 2 x x − + 6 5 is even, then x is odd.