5. (15) Verify each of the following using a truth table and clearly explain what the...

Transcribed Image Text:

5. (15) Verify each of the following using a truth table and clearly explain what the truth table shows. No points will be given if a full sentence (at least) explaining the results is not provided. a. An implication's converse is equivalent to its inverse. b. An implication is equivalent to its contrapositive. c. An implication is not equivalent to its converse. 6. (12) Write each of the following in symbolic notation (be sure to provide the dictionary for each) and determine whether each argument is valid using a separate truth table for each. Every statement must be in the truth table - do not skip any steps or you will not get full credit. Be sure to state in a sentence - not just a few words - whether or not the argument is valid and how you know from the results of the truth table. a. If it rains, then I take an umbrella. If I take an umbrella, then I am not in fashion. Therefore, if it rains, then I am not in fashion. b. I land at Gander Airport or I land at JFK Airport. If I land at Gander Airport, then I will miss the Rangers game. If I land at JFK Airport, then I will not kiss a fish. Therefore, I will either kiss a fish or I will miss the Rangers game. 5. (15) Verify each of the following using a truth table and clearly explain what the truth table shows. No points will be given if a full sentence (at least) explaining the results is not provided. a. An implication's converse is equivalent to its inverse. b. An implication is equivalent to its contrapositive. c. An implication is not equivalent to its converse. 6. (12) Write each of the following in symbolic notation (be sure to provide the dictionary for each) and determine whether each argument is valid using a separate truth table for each. Every statement must be in the truth table - do not skip any steps or you will not get full credit. Be sure to state in a sentence - not just a few words - whether or not the argument is valid and how you know from the results of the truth table. a. If it rains, then I take an umbrella. If I take an umbrella, then I am not in fashion. Therefore, if it rains, then I am not in fashion. b. I land at Gander Airport or I land at JFK Airport. If I land at Gander Airport, then I will miss the Rangers game. If I land at JFK Airport, then I will not kiss a fish. Therefore, I will either kiss a fish or I will miss the Rangers game.