91影视

Show that if \(p, q,\) and \(r\) are compound propositions such that \(p\) and \(q\) are logically equivalent and \(q\) and \(r\) are logically equivalent, then \(p\) and \(r\) are logically equivalent.

Exercises \(61-64\) are based on questions found in the book Symbolic Logic by Lewis Carroll. Let P(x), Q(x), and R(x) be the statements 鈥渪 is a clear explanation,鈥� 鈥渪 is satisfactory,鈥� and 鈥渪 is an excuse,鈥� respectively. Suppose that the domain for x consists of all English text. Express each of these statements using quantifiers, logical connectives, and P(x), Q(x), and R(x). a) All clear explanations are satisfactory. b) Some excuses are unsatisfactory. c) Some excuses are not clear explanations. d) Does (c) follow from (a) and (b)?

Exercises \(61-64\) are based on questions found in the book Symbolic Logic by Lewis Carroll. Let P(x), Q(x), R(x), and S(x) be the statements 鈥渪 is a baby,鈥� 鈥渪 is logical,鈥� 鈥渪 is able to manage a crocodile,鈥� and 鈥渪 is despised,鈥� respectively. Suppose that the domain consists of all people. Express each of these statements using quantifiers; logical connectives; and P(x), Q(x), R(x), and S(x). a) Babies are illogical. b) Nobody is despised who can manage a crocodile. c) Illogical persons are despised. d) Babies cannot manage crocodiles. e) Does (d) follow from (a), (b), and (c)? If not, is there a correct conclusion?

Construct a compound proposition that asserts that every cell of a \(9 \times 9\) Sudoku puzzle contains at least one number.