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Show that the following statement pattern is contingency. (p → q) ∧ (p → r) - Mathematics and Statistics

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Question

Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)

Sum
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Solution

p q r p→q p→r (p→q)∧(p→r)
T T T T T T
T T F T F F
T F T F T F
T F F F F F
F T T T T T
F T F T T T
F F T T T T
F F F T T T

The truth values in the last column are not identical. Hence, it is contingency.

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Chapter 1: Mathematical Logic - Exercise 1.6 [Page 16]

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