Complete the truth table for the logical statement ~p ^ q. р д-р ~рла TT LL FL TFF FTT F F LL F FFT T О р 9-р ~рла TTF Τ TFF FL FTT Τ FFT T O р 9-р ~рла TTF TF FL FL FTT T T FFT F O р 9-р ~рла TTF TFF FTT FFT LL F LL F T LL F

Complete the row of each truth table. Use T for true and F for false, b ~a^b cv(~ anb) C аль | T F ~p ~ (qv~p) - (qv ~p)ar r qu~p F. F T. T

2.2.4 Exercises 1. Construct the truth tables for the following compound statements: (а) р^(qVr). (b) ¬(p V (¬q)]^r. (c) (r ^p) V –¬q. (d) (р^9) V (р^г).

Which ones are true and which ones are false

1. Determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. a. r^~(p V r) 2. Use two truth tables to show that each of the statements are equivalent. a. p V (q Ar), (p V q) ^ (p r) 3. Construct a truth table for each compound statement a. (p V q) A [~(p V ~q)]

Determine the truth value of each compound statement when p is true, q is false, andris false. -p V (q ^ r) (-p ^ r) ^ q ? ? (-ял -р) V -r ? (-p V -q) V ~r ? (p ^ -q) V r

The domain of a certain exponential function is all real numbers. The range of the function is all real numbers greater than -3. The graph of the function has a horizontal asymptote at y = -3. Select a graph or graphs to fit the description of the function. -10 -9 -8 -7 -6 -5 -4 -2 y 10+ 9- 8 6 7+ -1-1+ -2+ -3- -4 5 6- 5- 4 4- 3 2 3 1 -10- y 10- 9 8 -5- -6- -7- 7- 8+ -9++ 2 4 6 -7 8 -10 X

Watch the video and then solve the problem given below. Click here to watch the video. Complete a truth table for (p^~ q) ~p. Enter the final column. Р ~p -q T T T F F T F F T T F F ... (PAq) (p^ q) ^ ~p F T F K

Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. ◆ (a.) The logic expressions (p → (q→r)) and ((p ^ q) →r) are logically equivalent. ◆ (b.) Suppose the proposition p V q is true, but we do not know which of p or q is true. If p→r and q→ r, then regardless of which of p or q is true, then we can infer proposition r to be true. ♦ (c.) Let A be a finite set of n elements. Then the number of subsets of A is n². (d.) If the symmetric difference of two sets is empty, then those two sets are equal. + (e.) Consider the divides relation x Ryxy. If R is defined over the set of all integers Z, then R is a partial-order relation. ♦ (f.) Let X and Y be finite sets. If there exists a function f : X→ Y that is one-to-one, then X ≤ Y powerset P(S) is also countable. ◆ (g.) If a set S is countable, then its (h.) The infinite union of finite sets is countable. → (i.) Let F(x)= automorphism on (R+, .) - x². F is an ♦ (j.) The set of non-zero real numbers with…

5. Use a truth table to evaluate (p ^ q) → r = ~p V (~q v r). Each column should be headed by a full statement, not an abbreviation such as →'. You do not need to fill all columns. pqr a TTT b TTF c T|FT d TFF e FTT f F TF g F F T hFFF Write a sentence or two explaining whether two statements are logically equivalent or not. You may use the letters on the left side to reference a row in your explanation.