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Using the basic identities of Boolean algebra, show that: xy + x'z + yz = xy + x'z

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Final answer:

To show that xy + x'z + yz simplifies to xy + x'z, we use the consensus theorem of Boolean algebra which indicates yz is redundant and can be eliminated, thus simplifying the expression.

Step-by-step explanation:

To prove that xy + x'z + yz is equal to xy + x'z using basic identities of Boolean algebra, we will apply the consensus theorem which states that AB + A'C + BC = AB + A'C. This is analogous to the provided equation if we align A with x, B with y, and C with z.

Following the consensus theorem, yz can be eliminated from the expression because it is redundant when combined with xy (covering the case where y is true) and x'z (covering the case where z is true). Thus, we simplify xy + x'z + yz to xy + x'z.

This illustrates that the original expression has unnecessary terms once we understand the overlapping coverage provided by each product term in the context of Boolean algebra.

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