b. Proof using Induction. 4" – 1 - 1+4+4? + · . . + 4"-1 3
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- not handwritten 4-Compute the weakest precondition for the following statements A. A. x = 8x +( 2 y + 4x); y=4*x+ 4 {y > 16} B. if (x > y) y=2*x+ 4 else y= 6 * x+3; {y > 3}44. What is the value of the following expression:24//6%3, 24//4//2 a. (1,3) b. (0,3) c. (1,0) d. (3,1)State (in words) the negation of the following statements.1. (∃x ∈ Z)P(x) ∧ (∀y ∈ R)(¬Q(y)).
- Prove the following arguments. Use INDIRECT PROOF:1) A → ( B ۸ C )2) B → ( D ۸ E )_____________Therefore: A ۷ DIndicate what proof technique you'll use to proof this statement then proof the statement. For all integers a, b, and c, if a, b, and c are consecutive, then a + b + c is even.Determine the truth value of each of the following statements. We assume that the domain for all variables consists of all integers. 1. n m (n2< m)2. n m (n < m2)3. n m (n + m = 0)4. n m (nm = m)5. n m (n2+ m2= 5)6. n m (n2+ m2= 6)7. n m (n + m = 4 n – m =1)8. n m (n + m = 4 n – m =2)9. n m p (p = (m + n)/2)
- Compute the weakest preconditions of the following statements for the given postconditions. Assume all variables are integers.(a) a = 2*b + 1;b = a*a + 1;{ a > 10 } (b) if (b > 0)a = 4*b - 10;elsea = b + 172;{ a > 0 }42. Consider the expression given below. The value of X is:X = 2+9*((3*12)-8)/10 a. 30.0 b. 30.8 c. 28.4 d. 27.2Compute the weakest preconditions of the following statements for the given postconditions. Assume all variables are integers1)a = 2*b + 1;b = a*a + 1;{ a > 10 } 2)if (b > 0)a = 4*b - 10;elsea = b + 172;{ a > 0 }
- Write these statements using ^and, V or, ~not P ↑ Q P ---> Q P <---> Q1. Compute the weakest preconditions of the following statements for the given postconditions. Assume all variables are integers. (a) a = 2*b + 1; b = a*a + 1; { a > 10 } (b) if (b > 0) a = 4*b - 10; else a = b + 172; {a>0}Implement the following Boolean expressions as they are stated: (a) X = ABC + AB + AC (b) X = AB(C + DE)