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Magazine Problem 8
Negate the following sentences. If \(x\) is a rational number and \(x \neq 0,\) then \(\tan (x)\) is not a rational number.
Problem 10
Negate the following sentences. If \(f\) is a polynomial and its degree is greater than \(2,\) then \(f^{\prime}\) is not constant.
Problem 10
Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " The discriminant is negative only if the quadratic equation has no real solutions.
Problem 11
Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " You fail only if you stop writing. (Ray Bradbury)
Problem 12
Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " People will generally accept facts as truth only if the facts agree with what they already believe. (Andy Rooney)
Problem 12
Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. If the integer \(x\) is a multiple of 7 , then it is divisible by 7 .
Problem 12
Translate each of the following sentences into symbolic logic. You can fool some of the people all of the time, and you can fool all of the people some of the time, but you can't fool all of the people all of the time. (Abraham Lincoln)
Problem 14
Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. Call me Ishmael.
Problem 14
Decide whether or not the following pairs of statements are logically equivalent. \(P \wedge(Q \vee \sim Q)\) and \((\sim P) \Rightarrow(Q \wedge \sim Q)\)
