(1) Prove the identity of each of the following Boolean equations using algebraic manipulation. (a) X'Y' + X'Y + XY = X'+Y (b) A'B + B'C' + AB + B'C = 1 (c) Y + X'Z + XY' = X +Y + Z
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- Computer science need correct Answer Simplify the following algebra expressions, (i) x'+y'+ xyz' (ii) A + A'B + A'B'C + A'B'C'DComputer Science: Use appended Table to show that the following Boolean identities are satisfied. Boolean variable and/or Boolean expressions postfixed with ’ symbol are considered negated. For instance, X’ is equivalent to NOT X.a. X + ( X’ Y + X Y )’ = X + Y’b. (( X Y ) Z ) + ( Y Z ) = Y Zc. X’ Y = X’ Y + X’ Y Zd. (X + Y) = XYZ’ + XY’Z’ + X’YZ’Simplify the following Boolean expressions to a minimum number of literals indicating theorems used for each step . 1. ABC + A 'B + ABC' 2. x'yz + xz 3. (x + y)'(x' + y') 4. xy + x(wz + wz') 5. (BC' + A' D)(AB' + CD ')
- 2. Simplify the following Boolean expressions, using three variable K-maps: (a) F(x,y,z) = xy+x′y′z′+x′yz′ (b) F(x,y,z) = x′y′+yz+x′yz′ (c) F(x,y,z) = x′y+yz′+y′z′Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step. a) F(x,y,z) = y(x' + (x + y)')b) F(x,y,z) = x'yz + xzc) F(x,y,z) = (x' + y + z')' + xy'z' + yz + xyzValidate/ prove that the following Boolean Laws/Theorems are the equal/same using the Truth Table: 2. X.Y + X'.Z + Y.Z = X.Y + X'.Z
- Simplify the following equation using Boolean Identities: ~x~yz + ~xy~z + x~y~z + x~yz + xy~z + xyz Construct truth tables for the following: xyz+ x~(yz) + ~(xyz) (x + y)(x + z)(~x + z) Use the truth tables from the previous question to create equations in SOP and POS format. Develop truth tables for the following equations: a) (A+B)(B+C)b) ~A(B + C)c) (A+B)^(CD)Given the Boolean function F below, reduce it to a simplest form using identity laws. Provide step-by-step activities along with the identity used at each step. F(X,Y,Z)= X’Y’Z + X’YZ + XY’Z + XYZQuestion 6 Computer Science Simplify the following Boolean Algebra expression using Boolean Identities (where ' means "not") (A+B+C+D')(E+A)(E'+B+C+D')
- Question 4the complement of the following logical expression xy'+ywUsing the laws of boolean algebra simplify these expressions and LIST the laws used to justify each step. . Each final result should be expressed as a sum of products of literals, where each product uses the smallest number of literals. a. ABC + ABC’ + A’C + A’B’C + AB’C b. A'B' + A'BC' + (A + C')' c. A' + A'B'CD' + A'B'C'D' + AB'C' + AB'CD' + ABD + BC'DShow that the argument is valid, indicating the rule of inference or logical equivalence applicable to each step. ∃x ( C(x) ∧ ( ¬ S(x) → ( V(x) ∨ W(x) ) ) )∀x ( V(x) → ¬ C(x) )¬ ∃x ( W(x) ∧ C(x) ) _________________________∴ ∃x ( S(x) ∧ ¬ W(x) )