1. Give a truth table that shows the (Boolean) value of each of the following Boolean expressions, for every possible combination of "input" values. Hint: including columns for intermediate expressions is helpful a not (P and Q) Pand Q Not (P and Q) F F b. (not P) and Q P. (Not P) and Q not P T. F F.
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- Build truth tables or abbreviated truth tables (on your own scratch paper) to determine whether the following arguments are valid or invalid. (A v B) --> (C • D), (X v ~Y) --> (~C • ~W), (X v Z) --> (A • E), ∴∴~X Group of answer choices A. Valid B. InvalidConstruct a truth table for the statements belowa. (p ∧ q) ∧ (~r ∨ q).b. ~[~p ∧ (q ∧ r)]c. [p ∧ (q ∨ ~p)] → ~p then find the truth value of the statement givena. p is a false statement, q is a true statement and r is a true statement.b. p is a false statement, q is a false statement and r is a false statement.c. p is a false statement, q is a false statement and r is a true statement.Simplify the following expression using Boolean algebra rules and create a truth table for the simplified expression: Are the two expressions equivalent?Explain.
- Show using a truth table if the following statements are equivalent. d. p → (q ∨ r) and (p → q) ∨ (p → r)e. [p ↔ (q ∨ r)] ∨ q and (p → q) ∨ (p ↔ r)Are the statements P → (Q ∨ R) and (P → Q)⋁(P → R) logically equivalent? Create a truth table.Create truth tables for the following expressions:a. S = NOT((A OR B) AND (NOT(A) OR NOT(B)))b. S = (A AND B) OR NOT(A OR B)c. S = (A) OR (B AND C) OR (NOT(B OR C) AND (A OR C))d. S = ((A AND B) OR (C AND D)) AND NOT((C AND NOT(A)) OR (B AND D))
- Construct a truth table and use it to determine which of the following statements is equivalent to the statement ∼p∧∼q.i need answer of all. if any answer will be skipped, your answer will be rejected. only complete answer will be accepted. b) Make a truth table for the statement ¬P ∧ (Q → P). What can youconclude about P and Q if you know the statement is true? a) Make a truth table for the statement (P ∨ Q) → (P ∧ Q). c) Make a truth table for the statement ¬P → (Q ∧ R).The following argument is quantificationally valid. Explain why. (∀x)(Sx ⊃(Gx ∨Bx))(∃x)(Sx & ~ Bx) (∃x)Gx Can you explain in words not symbols?
- Using the test technique(for example, replace E with symbol a... ), prove or disprove the following identities concerning regular expressions.1. (E + F)∗ = (E∗ + F∗)∗2. (EE)∗ = E∗ + E^2Construct a truth table that displays all possible values for the following expression: ~p ^ ( ~p V q ) -> ( p V q ) **Provide a list for the order of the operators that should be evaluatedCorrect answer will be upvoted else downvoted. Computer science. decimal portrayal of x without driving zeroes comprises of a digits; the decimal portrayal of y without driving zeroes comprises of b digits; the decimal portrayal of gcd(x,y) without driving zeroes comprises of c digits. gcd(x,y) indicates the best normal divisor (GCD) of integers x and y. Output x and y. In case there are various replies, output any of them. Input The primary line contains a solitary integer t (1≤t≤285) — the number of testcases. Every one of the following t lines contains three integers a, b and c (1≤a,b≤9, 1≤c≤min(a,b)) — the necessary lengths of the numbers. It very well may be shown that the appropriate response exists for all testcases under the given limitations. Extra requirement on the input: all testcases are unique. Output For each testcase print two positive integers — x and y (x>0, y>0) to such an extent that the decimal portrayal of x without…