Question

15. Find two open sentences \( P(n) \) and \( Q(n) \), both over the domain \( S=\{2,4,6,8\} \), such that \( P(2) \) and \( Q(2) \) are both true, \( P(4) \) and \( Q(4) \) are both false, \( P(6) \) is true and \( Q(6) \) is false, while \( P(8) \) is false and \( Q(8) \) is true. 16. Find an open sentence \( P(n) \) over the domain \( S=\{3,5,7,9\} \) such that \( P(n) \) is true for half of the integers in \( S \) and false for the other half. 17. State the negation of each of the following statements. (a) At least two of my library books are overdue. (b) One of my two friends misplaced his homework assignment. (c) No one expected that to happen. (d) It's not often that my instructor teaches that course. (e) It's surprising that two students received the same exam score.

          15. Find two open sentences \( P(n) \) and \( Q(n) \), both over the domain \( S=\{2,4,6,8\} \), such that \( P(2) \) and \( Q(2) \) are both true, \( P(4) \) and \( Q(4) \) are both false, \( P(6) \) is true and \( Q(6) \) is false, while \( P(8) \) is false and \( Q(8) \) is true.
16. Find an open sentence \( P(n) \) over the domain \( S=\{3,5,7,9\} \) such that \( P(n) \) is true for half of the integers in \( S \) and false for the other half.
17. State the negation of each of the following statements.
(a) At least two of my library books are overdue.
(b) One of my two friends misplaced his homework assignment.
(c) No one expected that to happen.
(d) It's not often that my instructor teaches that course.
(e) It's surprising that two students received the same exam score.

15. Find two open sentences P(n) and Q(n), both over the domain S={2,4,6,8}, such that P(2) and Q(2) are both true, P(4) and Q(4) are both false, P(6) is true and Q(6) is false, while P(8) is false and Q(8) is true.
16. Find an open sentence P(n) over the domain S={3,5,7,9} such that P(n) is true for half of the integers in S and false for the other half.
17. State the negation of each of the following statements.
(a) At least two of my library books are overdue.
(b) One of my two friends misplaced his homework assignment.
(c) No one expected that to happen.
(d) It's not often that my instructor teaches that course.
(e) It's surprising that two students received the same exam score.

Added by Joel W.

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