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Math homework Week 2

Math homework Week 2 - F T F T T T F T F T F F T F F F F F...

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Use Mathematical Induction proof to prove expression: 11 * + 2 12 * + 3 ..... + 1n * ( + ) n 1 = + nn 1 , n≥ 1 n=1 11 * + 1 1 = 11 * 2 n=2 12 * + 2 1 = 12 * 3 So, change the equation to include a k. 1k * + k 1 ; 1k * + k 1 + + + + 1k 1k 1 1 or + ( + ) 1k 1 k 2 = + + k 1k 2 Then to do the other side of the problem ..... + kk 1 + + ( + ) 1k 1 k 2 = + + + ( + ) kk 2 1k 1 k 2 = + + + ( + ) k2 2k 1k 1 k 2 = + + + + k 1k 1k 1k 2 = + + k 1k 2 Proved by induction Construct a truth table to show that expression → (~ ) q p p q is a tautologies q p q p ~ p (~ ) p q → (~ ) q p p q T T T F F T

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T F F T T T F T T F F T F F T T F T Construct a truth table to show that expression p q r and ( ) → p r q r are logically equivalent p q r p q r p q T T T T T T F F T F T T T F F T F T T T F T F F F F T T F F F F ( ) p r q r p r q ( ) → p r q r T T T T
T T F T T F T F T F F T F T T T F T
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Unformatted text preview: F T F T T T F T F T F F T F F F F F right now it does not look like they are equivalent, but if you re-arrange the rows to correspond with the top it would look the same. For instance, if you look at the first table [ → → p q r ], 2nd row you see that the p=t, q=t, r=f and the last column=f. If we find the same row in the table below where p=t, q=t, r=f, the last column for that row also =f; by rearranging the rows it would look like this: p q r ( ) → p r q r T T T T T T F F T F T T T F F T F T T T F T F F F F T T F F F F...
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