Let q = be two rational numbers written in lowest terms. Let d s=q+rands= =; be written in lowest terms. Assume that s is not 0. Prove or disprove the following two statements. a. If b and d are odd, then f is odd. b. If b and d are even, then f is even. and r =

Write equivalent expressions for each of the following by using De Morgan’s Law.   A. !(x < 5) B. !(y > 2 && !found ) C. !(c == ‘r’ || (( y > 2) && !found ))

Tell if the statements are true or false. Let  p: 2 + 1 = 3; q: 16 − 9 = 7. (a)     ~p ∨ q TrueFalse     (b)     ~p ∧ ~q TrueFalse     (c)     ~(p ∧ q) TrueFalse

Consider the following statement: Statement A: ∀ integers m and n, if 2m + n is odd then m and n are both odd. Disprove Statement A. That is, show that Statement A is false

2. Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. If true, give a brief explanation for why. If false, give a counterexample (i.e. a set of values x,y that make the statement false. You must also explain why they make the statement false.) a) yvx((y > x²) → y > x) b) Vy!x(√√ 0)) d) x(x < 0⇒x² ≥y) e) \xy(x² = y² ↔ y³ = x³)

What does the statement 'guess == 5' do? a. assigns the value 5 to guess b. if guess is not equal to 5, it assigns 5 to guess. If it is equal, it leaves guess alone. c. tests for inequality, resulting in True when guess is not equal to 5 d. tests for equality, resulting in True when guess is equal to 5   What does 'num > 5' test for? a. the value in num is greater than or equal to 5 b. the value in num is greater than 5 c. the value in num should be greater than 5 d. num will be set to 5   How are letters stored in memory? a. as ones and zeros using ASCII encoding b. directly c. letters cannot be stored in memory d. using public key encryption

PS: Please complete all of the subparts as they are all the same question and not in Handwritten paper.

Identify p, g, and r if necessary. Then translate each argument to symbols and use a truth table to decide if the argument is valid or invalid. If it snows, I can go snowboarding, It did not snow . I cannot go snowboarding.

Q: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.”  b→(s→¬v)     2. b→(s∧¬v)   3. s∧(¬v→b) 4.  (s∧¬v)→b Group of answer choices b→(s∧¬v) b→(s→¬v) s∧(¬v→b) (s∧¬v)→b   2);  The following two statements are logically equivalent   (p → q) ∧ (r → q) and (p ∧ r) → q Group of answer choices True False

2. Prove that if x and y are real numbers, then max(x, y) + min(x, y) = x + y.[Hint: Use a proof by cases, with the two cases corresponding to x > y and x < y,respectively.]