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- 2a - Determine the weakest precondition for the following sequence of expressions. Pleaseprovide all your work including calculations, logic implications if any applies, and final answer.(10 points){ ? } a = 4 * (3 * b - a); b = 4 * a - 6; { b > 10 }2b - Determine the strongest precondition for the following if-else statement. Please provide allyour work including calculations, logic implications if any applies, and final answer. (15 points){ ? } if (x > y) then y = 2 * x - 1 else y = 3 * x + 1; {y>7}If the statements p and q are both true while statement r is false. which of the following has a false truth value?* a. If r then (p or q). b. Not (r and (not p or q)). c. (p or r) if and only if not q. d. If not (r and q) then p.1. Give the unifyiing substitition for (x,y,z are variables): f(a) f(b) 2. Give the unifyiing substitition for (x,y,z are variables): g(x,x) g(f(a),f(y)) 3. Give the unifyiing substitition for (x,y,z are variables): g(x,x) g(f(a0,f(b))
- If, A = {3, 5, 7, 9} B = {2, 4, 6, 8, 10} C = {12, 14, 18, 20, 24} D = {21, 26, 31, 36} A. State whether TRUE or False: 1. 13 ∈ C 2. 6 ∉ A 3. 31 ∈ D 4. 20 ∉ B B. Fill in the blanks to make each statement true: 5.) 3 ∈ ___ 6.) 4 ___ B 7.) 26 ___ C 8.) 8 ∈ ___Make use of De Morgan’s Laws to write the given statement in an equivalent form. 6. It is not true that Bob failed the English proficiency test and he registered for a speech course.Unify the following atomic formulas. Indicate Fail if they cannot be unified. Variables and functions are indicated by lower case; constants are indicated by upper case. 1. P(x, y, y, z) P(Apple, Banana, w, w) 2. P(y, x, f(y)) P(z, w, z) 3. P(x, f(x), x) P(Apple, f(w), y)
- Let p, q, and r represent the following statements: p: The first ball is red. q: The second ball is white. r: The third ball is blue. Which would be the correct English statement for the symbolic form (¬¬p ∧∧ q) →→ r ? Group of answer choices A .If the first ball is red or the second ball is white, then the third ball is blue. B. If the first ball is not red or the second ball is white, then the third ball is blue. C .If the first ball is not red and the second ball is white, then the third ball is blue. D. If the first ball is red and the second ball is white, then the third ball is blue.Given: If A AND B, then C. Given: The if-then statement's reverse is also correct. If A is True, B is True, what is C? Forward and reverse / Forward and reverse Not True or False False TrueSolve the following questions: a)Solve the following postfix expressions i)2 3 + 1 - ii)3 4 - 10 + 7 2 3 * - 9 * /a) Convert the following infix to postfix expressions i)2 * 3 - 5 / 2 + 4 ii)1 * 2 * 3 * 4
- Determine if the following statements are logically equivalent:p ∨ (q ∧ r),(p ∧ q) ∨ (p ∧ r)Variables: p,q,rDetermine the truth value of the statement (~p ∨ q) ∨ (r ∧ q) using the following conditions. a) p is false, q is true, and r is true. b) p is true, q is false, and r is false. a) If p is false, q is true, and r is true, what is the value of (~p ∨ q) ∨ (r ∧ q)? True? False? b) If p istrue, q is false, and r is false, what is the value of (~p ∨ q) ∨ (r ∧ q)? True? False?Given the constants and variable declarations #define PI 3.14159 #define MAX_I 1000 . . . double x, y; int a, b, i; ( Indicate which of the following statements are valid, and find the value stored by each valid statement. Also, indicate which are invalid and why. Assume that a is 3, b is 4, and y is −1.0. i=a%b; i=(989−MAX_I)/a; i=b%a; x=PI*y; valid i=a/−b; x=a/b; x=a%(a/b); i=b/0; i=a%(990−MAX_I); i=(MAX_I−990)/a; x=a/y; i=PI*a; x=PI / y; x=b/a; i=(MAX_I−990)%a; i=a%0; i=a%(MAX_I−990); x=(double) a/b;