ei 3. 4. Let p, q, and r be the propositions: p: You are sick. q:...

  

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ei 3. 4. Let p, q, and r be the propositions: p: You are sick. q: You miss the final examination. r: You pass this subject. Express each of the following propositions as an English sentence. (a) p=q (b) -q=r State the converse and contrapositive of each of the following implications. (a) If it does not rain tonight, I will go fishing tomorrow. (b) If it rains tonight, then I will stay at home. Find the bitwise OR, bitwise AND, and bitwise XOR of each pair of bit strings. (a) 1011110, 0100001 In general, a statement involving n variables x,xx, can be denoted by P(x,,.,x) and is the value of the predicate P at the n-tuple (xx). (a) Suppose Q(x,y) denotes the statement" x=y+3." What are the truth values of the propositions Q(1,2) and Q(3,0)? (b) Let R(x,y,z) denote the statement "x+y=z." What are the truth values of R(1,2,3) and R(0,0,1)? 5. Determine whether the following arguments are valid or not. If an argument is valid, which rule of inference is used? If not, which fallacy occurs? (a) If n is a real number such that n>1, then n>1. Suppose that n>1. Then n>1. (b) The number log, 3 is irrational if it is not the ratio of two integers. Therefore, since log, 3 cannot be written in the form of where a and b are integers, it is irrational. ei 3. 4. Let p, q, and r be the propositions: p: You are sick. q: You miss the final examination. r: You pass this subject. Express each of the following propositions as an English sentence. (a) p=q (b) -q=r State the converse and contrapositive of each of the following implications. (a) If it does not rain tonight, I will go fishing tomorrow. (b) If it rains tonight, then I will stay at home. Find the bitwise OR, bitwise AND, and bitwise XOR of each pair of bit strings. (a) 1011110, 0100001 In general, a statement involving n variables x,xx, can be denoted by P(x,,.,x) and is the value of the predicate P at the n-tuple (xx). (a) Suppose Q(x,y) denotes the statement" x=y+3." What are the truth values of the propositions Q(1,2) and Q(3,0)? (b) Let R(x,y,z) denote the statement "x+y=z." What are the truth values of R(1,2,3) and R(0,0,1)? 5. Determine whether the following arguments are valid or not. If an argument is valid, which rule of inference is used? If not, which fallacy occurs? (a) If n is a real number such that n>1, then n>1. Suppose that n>1. Then n>1. (b) The number log, 3 is irrational if it is not the ratio of two integers. Therefore, since log, 3 cannot be written in the form of where a and b are integers, it is irrational.