A logic operator not defined in this chapter is the NAND function; it is denoted by. NAND is short for “not AND” where a _ b = ~ (a ^ b).

a. Give the truth table for the two-input NAND function

b. Show that the NAND operator can be used to simulate each of the AND, OR, and NOT operators.

Use the propositional logic to represent the following English sentences. Choose appropriate propositional logic variables.

a. Many Americans have difficulty learning a foreign language.

b. All sophomores must pass an English language proficiency exam in order to continue their studies.

c. If you are old enough to join the military, then you should be old enough to drink.

d. A natural number greater than or equal to two is prime if and only if it has no divisors other than 1 and itself.

e. If the price of gasoline continues to rise, then fewer people will be driving this summer.

f. If it is neither raining nor snowing, then it is likely there is no precipitation.

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