Simplify the following expressions by applying Boolean rules. M [ N (M+N) ]
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- Given the following definitions: U={a,b,c, d, e, f, g} A={a, c, e, g} B={a,b,c,d} find A n BShow that the following statements are equivalent, where n is an integer greater than or equal to 2. Feel free to consider any of the following pairs. 1. “n is even” and “n – 1 is odd”2. “n is even” and “n2 is even”3. “n – 1 is odd” and “n2 is even” with Step By step explanation pleaseasymptotic analysis/notation Find the value of c, and n such that 2n log n + 5n2 is Ω(n2)
- Describe the following sets by regular expressions, (a) {abba} (b) {a, ab} .Simplify the following logic formulas. Use a truth table to show that your simplification is correct. (a.) (p∧q)∨q(p∧q)∨q (b.) p→(p→q)p→(p→q) (c.) ¬(¬p∧¬q)¬(¬p∧¬q) "Simplify" means: find the simplest/smallest formula that means the same thing.Using n as the input size, what is the running time of the following algorithm?
- Simplify the following expressions according to the commutative law: a. A⋅B + B⋅A + C⋅D⋅E + C⋅D⋅E + E⋅C⋅D b. A⋅B+A⋅C+B⋅A c. (L⋅M⋅N) (A⋅B) (C⋅D⋅E) (M⋅N⋅L) d. F⋅(K + R) + S⋅V + W⋅X + V⋅S + X⋅W + (R + K)⋅FShow that the following statements are equivalent, where n is an integergreater than or equal to 2. “n is even” and “n – 1 is odd”2. “n is even” and “n2 is even”3. “n – 1 is odd” and “n2 is even”Simplify the following expressions in normal form, if one exists: (λq. q q)(λs. s s a)
- Construct a truth table for ~[ (p ↔ q) ^ (r v ~p) ] → ~q. please use T or F.Which of the following statements in the picture below can be applicable to dijkstra's algorithm but not prim's algorithm?(proof by contraposition) If the product of two integers is not divisible by an integer n, then neither integer is divisible by n