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ScanSolve AI Tutor · Accepted Answer

To prove the Boolean identity A + AB = A + B, we will start with the left-hand side and simplify it using the laws of Boolean algebra. Step 1: Start with the left-hand side of the equation. A + AB Step 2: Apply the Distributive Law, which states that X + YZ = (X+Y)(X+Z). Here, X=A, Y=A, and Z=B. A + AB = (A + A)(A + B); Step 3: Use the Complement Law, which states that A + A = 1. (A + A)(A + B) = 1 · (A + B); Step 4: Apply the Identity Law, which states that 1 · X = X. 1 · (A + B) = A + B Conclusion: We have shown that the left-hand side is equal to the right-hand side. A + AB = A + B The identity is therefore proven. The identity A + AB = A + B is proven.

Solve this showing all the steps, in English

Step-by-step solution

Start with the left-hand side of the equation.

Apply the Distributive Law, which states that $X + YZ = (X+Y)(X+Z)$ .

Use the Complement Law, which states that $A + \overline{A} = 1$ .

Apply the Identity Law, which states that $1 \cdot X = X$ .

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More English Questions

Solve this showing all the steps, in English

Step-by-step solution

Start with the left-hand side of the equation.

Apply the Distributive Law, which states that X+YZ=(X+Y)(X+Z)X + YZ = (X+Y)(X+Z)X+YZ=(X+Y)(X+Z).

Use the Complement Law, which states that A+A‾=1A + \overline{A} = 1A+A=1.

Apply the Identity Law, which states that 1⋅X=X1 \cdot X = X1⋅X=X.

Still stuck on this one?

More English Questions

Apply the Distributive Law, which states that $X + YZ = (X+Y)(X+Z)$ .

Use the Complement Law, which states that $A + \overline{A} = 1$ .

Apply the Identity Law, which states that $1 \cdot X = X$ .