P Q True Say P Sufficient Condition Q Words Know P Q P True Sufficient Conclude Q Also Tru Q43890564
When P Q is true, we say that P is a sufficient condition for Q. In other words, if I know that P Q and P are true this is sufficient for me to conclude that Q is also true. Let x represent an unknown integer. Give a sufficient condition for the statement “x/2 is an integer”. When P Q is true, we say that Q is a necessary condition Cor P. In other words, if I know that P Q is true and that Q is false then I can conclude that P must be false. Let n represent an unknown integer. Give a necessary but not sufficient condition for the statement “n + 2 is prime”. Let o be a new Boolean function, defined by the following truth table: AB AOB True True False True False True False True True False False True (a) Using only and the proposition A, find an expression logically equivalent to A. Demonstrate this logical equivalence with a truth table. (b) Using only o and the propositions A, B, find an expression log- ically equivalent to A AB. Demonstrate this logical equivalence with a truth table. Show transcribed image text When P Q is true, we say that P is a sufficient condition for Q. In other words, if I know that P Q and P are true this is sufficient for me to conclude that Q is also true. Let x represent an unknown integer. Give a sufficient condition for the statement “x/2 is an integer”. When P Q is true, we say that Q is a necessary condition Cor P. In other words, if I know that P Q is true and that Q is false then I can conclude that P must be false. Let n represent an unknown integer. Give a necessary but not sufficient condition for the statement “n + 2 is prime”. Let o be a new Boolean function, defined by the following truth table: AB AOB True True False True False True False True True False False True (a) Using only and the proposition A, find an expression logically equivalent to A. Demonstrate this logical equivalence with a truth table. (b) Using only o and the propositions A, B, find an expression log- ically equivalent to A AB. Demonstrate this logical equivalence with a truth table.
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