. Say for each of the following sets of statements if they are consistent or inconsistent. A.G Ↄ H / H Ↄ J / J Ↄ K/ K Ↄ ~G b. P ≡ Q / Q v P / P Ↄ X / Q Ↄ ~P c. Z Ↄ [(P ● R) v (L ● P)] / ~P Ↄ ~Z / L Ↄ~ R
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3
5. Say for each of the following sets of statements if they are consistent or inconsistent.
A.G Ↄ H / H Ↄ J / J Ↄ K/ K Ↄ ~G
b. P ≡ Q / Q v P / P Ↄ X / Q Ↄ ~P
c. Z Ↄ [(P ● R) v (L ● P)] / ~P Ↄ ~Z / L Ↄ~ R
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- Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample.Let A={8,9,10}, B={9,10,11,12,15} and C={9,10}. Which of the following statements are true? a) 5 ⊆ A b) C ⊆ B c) φ ∈ ADetermine if the following statements are logically equivalent:p ∨ (q ∧ r),(p ∧ q) ∨ (p ∧ r)Variables: p,q,r
- Let A={8,9,10}, B={9,10,11,12,15} and C={9,10}. Which of the following statements are true? a) d) {2,5} ⊆ A e) φ ⊆ CAssume that A and B are known to be true, X, Y, and Z are known to be false, and that the truth values of P and Q are unknown. For each of the following statements, state whether it is true or false (you have sufficient information even with the unknowns). P ® A ~ (P Q) v P (P ® X) ® (~X ® ~P)The force of gravitational attraction, F, of two bodies is given by a formula in which a constant, G, is multiplied by the product of the two masses (m1 and m2). This is then divided by the square of the distance, d, between the two bodies. Assuming these variables are declared, and have proper initial values where necessary, which of the following C++ statements correctly expresses this formula? a. F = = G*m1*m2/d^2; b. F = G*m1*m2/d*d; c. F = G*m1*m2*(d*d); d. None of the above
- Write a C++ fragment statements for each of the following: Printthe value of x and decrease x by 5 as long as x is positive. Readthe values for a, b and c and display their sum, repeating this as long as none of a, b or c is negative. Displaythe squares of the first 100 positive integers in increasing Printthe cubes of the first 50 positive integers in decreasing Displaythe square roots of the first 25 odd positiveConvert the following code into descriptive code, and verify using White Box Testing. int a[10]={23, 45, 10, 0, 98, 36, 2, 56, 34, 12}; for (int i=0; i a[j+1]) swap(&a[j], &a[j+1]); end-if end-for end-forSuppose that p and q are statements so that p → q is false. Find the truth values of each of the following. (a) ~p → q TrueFalse (b) p ∨ q TrueFalse (c) q → p TrueFalse
- Suppose we have the function g (n) = 6n + 5n2 + 3n3. Below are a number of statements regarding how the function grows depending on n. See pict Which / which of the above statements is true? Only statements A, B and F are correct Only statements A, C and E are correct Only statements B and D are correct Only statements B, C, D and F are correctCompute 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 the following compound statement in terms of the simple statements p, q, and r. "I go to office hours and ask questions, and my professor does not remember me." p: I go to office hours. q: I ask questions. r: My professor remembers me.