formulate 2 examples of compound statements under biconditional
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formulate 2 examples of compound statements under biconditional
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- Construct a truth table for the following compound statement, where p,q, and r denote primitive statementsDe Morgan’s laws state that specific Boolean statements can be written in different ways with the same meaning. A group of negated ANDs is the same as a negated group of ORs (!a && !b && !c) === !(a || b || c) A group of negated ORs is the same as a negated group of ANDs (!a || !b || !c) === !(a && b && c) Which construction would you use if your programming code needed to check if at least one of a,b,c is true? Which construction would you use if your programming code needed to check that a,b,c are all true? Explain your reasoning about choosing the programming code.Use De Morgan’s laws to determine whether the two statements are equivalent: ( ~ p ∨ ~ q ) → r , ~ ( p ∧ q ) → r
- Define Compound (Block of) Statements.Objective: The objective of this discussion is to be aware of the field of logic. Problem Statement: Show that the following statements are equivalent, where n is an integer greater than or equal to 2. consider the following pairs.1. “n is even” and “n – 1 is odd”2. “n is even” and “n(square2) is even”3. “n – 1 is odd” and “n(square2) is even”Complete the truth table for the given statements and then determine if the two statements are logically equivalent. ∼p∨∼q∼p∨∼q and p⇒∼q
- For each of the following statements about regular expressions α, β and languages A, B, state whether they are true or false. Provide a one-sentence justification for each answer.: Simplify the following Boolean expressions to a minimum * :number of literals F = abc + (a + c) + ābcWrite 20 examples of variable initialization
- Simplify the following Boolean expressions to a minimum number of literals: ( a + b + c ′ ) ( a ′ b ′ + c )2. Look for the dual of the following Boolean expressions:a. xyz + x'y'z'b. xz' + x⋅0 +x'⋅1Discrete Mathematics: Rewrite the statement formally using quantifiers and variables, and write a negation for each statement: 1. Everybody trusts somebody.