لمّاح✨ PMAU

Question 1: If p denotes "I study hard" and q denotes "I pass the exam", then q → p denotes A. I study hard if and only if I pass the exam. B. If I study hard, then I pass the exam. C. I pass the exam and I study hard. ✅ D. If I pass the exam, then I study hard. Question 2: The degree of the Boolean function f(w, x, y, z) = w x̄ + y z̄ is 4. ✅ True False Question 3: In Boolean Algebra, the value of (a + b̄)·(complement of ab), when a = 1 and b = 0, is A. 0 B. 2 ✅ C. 1 D. operation is not possible Question 4: The decimal expansion of the number with octal expansion (157)₈ is ✅ A. 111 B. 125 C. 157 D. 103 Question 5: If A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}, then A ∩ B = {2, 4, 6}. True ✅ False Question 6: Let A be the set of positive multiples of 3 less than 30, then the cardinality of A is: A. 10 B. 27 ✅ C. 9 D. 30 Question 7: In Insertion sort, to sort the elements 9, 4, 12, 1, 6 we must begin with the ……. element from the list. A. First ✅ B. Second C. Third D. Fourth Question 8: The sentence "x + 4 = 9" is a proposition. True ✅ False Question 9: Using Bubble sort, the list 3, 8, 2 becomes 2, 3, 8 after the first pass. True ✅ False Question 10: The proposition ¬(p ∨ q) is logically equivalent to A. ¬p ∨ q B. ¬p ∨ ¬q ✅ C. ¬p ∧ ¬q D. p ∨ q Question 11: Let f be the function from {p, q, r, s, t} to {−5, 3, 8, 0, 12} defined by f(p) = −5, f(q) = 3, f(r) = 8, f(s) = −5 and f(t) = 12, then the range of f is: ✅ A. {−5, 3, 8, 12} B. {−5, 3, 8, 0, 12} C. {−5, 8, 0, 12} D. {p, q, r, s, t} Question 12: The sum of two congruences 17 ≡ 3 (mod 7) and 23 ≡ 2 (mod 5) is: ✅ A. congruence sum is not possible B. 40 ≡ 6 (mod 7) C. 40 ≡ 5 (mod 5) D. 391 ≡ 6 (mod 7) Question 13: Let f(0) = 0 and f(n) = f(n − 1) + n² for n ≥ 1. What is f(5)? A. 30 ✅ B. 55 C. 91 D. 50 Question 14: The product of two positive integers is 2160 and their lcm is 360. What is their gcd? A. 4 B. 8 ✅ C. 6 D. 12 Question 15: The inverse of 5 modulo 11 is 9. ✅ True False