Boolean Algebra Practice Problems

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Questions and Answers

A + 0 = ______

a

W + (wxyz) = ______

w

(x + y)(x + y) = ______

x + y

A+ 0 =

<p>a</p> Signup and view all the answers

(a+b)(a+b) =

<p>a + b</p> Signup and view all the answers

A(a+b+c+ ...) =

<p>a</p> Signup and view all the answers

F[a,b,(ab)] =

<p>a + b + (ab)</p> Signup and view all the answers

(w+x+y+z)y =

<p>y</p> Signup and view all the answers

(x + y)(x + y) =

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W+[w+(wx)] =

<p>w</p> Signup and view all the answers

W+(wxyz) =

<p>w</p> Signup and view all the answers

Xz + xy + zy =

<p>xz + xy + zy</p> Signup and view all the answers

(x+z)(x+y)(z + y) =

<p>xz + xy + yz + xyz</p> Signup and view all the answers

Flashcards

a + 0 = a

The output is always the variable 'a'. Any variable added to a zero will always result in the original variable.

a • 0 = 0

The output is always 0. Any variable multiplied by zero will always result in zero.

a + a = a

The output is always the variable 'a'. When a variable is added to itself, it is the same as having one of that variable.

a • a = a

The output is always 'a'. When a variable is multiplied by itself, it is the same as having one of that variable.

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a + ab = a

The output is always 'a'. When a variable is added to the product of itself and another variable, the result is always the first variable.

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a(a + b) = aa + ab

The output is always 'a'. When a variable is multiplied by the sum of itself and another variable, the result is always the product of the two variables.

This is based on the distributive property: a(a + b) = aa + ab = a^2 + ab

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(a + b)(a + b) = (a + b)^2

The output is always (a + b)^2. When you multiply the sum of two variables by itself, you get the square of the first, plus twice the product of the two, plus the square of the second.

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a(a + b + c +... ) = a

The output is always 'a'. Any variable multiplied by the sum of itself and any number of other variables results in itself.

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f(a,b,ab)= a + b + ab = a + b

The output is always (a + b) since the last term 'ab' is already included in 'a + b'.

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f(a,b,ab)= a + b + ab = a + b

The output is always (a + b) since the last term 'ab' is already included in 'a + b'.

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f[a,b,(ab)]= a + b + c

The output is always (a + b + c) since the last term 'ab' is already included in 'a + b + c'. Therefore, the last term is redundant.

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y + yy = y

The output is always 'y'. When a variable is added to the product of itself and another variable, the result is always the first variable.

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xy + xy = xy

The output is always 'xy'. When the product of two variables is added to itself, it is the same as having one of those products.

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x + yx = x

The output is always 'x'. When a variable is added to the product of itself and another variable, the result is always the first variable.

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(w + x + y + z)y = y

The output is always 'y'. When the sum of any number of variables is multiplied by one of the variables, the result is always that single variable (since it is included in the sum).

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(x + y)(x + y) = (x + y)^2

The output is always (x + y)^2. When you multiply the sum of two variables by itself, you get the square of the first, plus twice the product of the two, plus the square of the second.

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w + [w + (wx)] = w

The output is always w. When a variable is added to the sum of itself again (including any other variable), the result is always the original variable.

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x[x + (xy)] = x

The output is always x. When a variable is multiplied by the sum of itself and any number of other variables, the result is always itself.

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x + x = x

The output is always 'x'. When a variable is added to itself, it is the same as having one of that variable.

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x * x = x

The output is always 'x'. When a variable is multiplied by itself, it is the same as having one of that variable.

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w + (wxyz) = w

The output is always 'w'. When a variable is added to the product of itself and any number of other variables, the result is always the original variable.

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w * (wxyz) = wxyz

The output is always 'wxyz'. When a variable is multiplied by the product of itself and any number of other variables, the result is always the product of all those variables.

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xz + xy + zy = xy + zy

The output is always 'xy + zy'. When a sum of multiple terms includes variables that are repeated in some of the terms, the result is always the sum of the terms with the least number of variables per product.

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(x + z)(x + y)(z + y) = (x + y)(z + y)

The output is always (x + y)(z + y). When a product of multiple sums includes variables that are repeated in some sums, the result is always the product of the sums with the least number of variables.

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x + y + xyz = x + y

The output is always 'x + y'. When the sum of multiple terms includes a product of those variables, the product is already included in the sum, and therefore is redundant.

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Study Notes

Boolean Algebra Practice Problems

  • a + 0 = a
  • a * 0 = 0
  • a + a = a
  • a * a = a
  • a + ab = a
  • a + ab = a
  • a(a + b) = a
  • ab + ab = ab
  • (a + b)(a + b) = a + b
  • a(a + b + c + ...) = a
  • For (11), (12), (13), f(a, b, c) = a + b + c
  • f(a, b, ab) = a + b
  • f(a, b, a-b) = a + b (Assuming the intended symbolic representation is for a NOT b which results in a + b)
  • f[a, b, (ab)] = a + b (Assuming the intended symbolic representation for complement of ab which results in a + b)
  • y + yy = y
  • xy + xy = xy
  • x + yx = x
  • (w + x + y + z)y = wy + xy + yz
  • (x + y)(x + y) = x + y
  • w + [w + (wx)] = w
  • x[x + (xy)] = x
  • (x + x) = x
  • (x + x) = x
  • w + (wxyz) = w
  • w * (wxyz) = wxy
  • xz + xy + zy = x + y + z
  • (x + z)(x + y)(z + y) = x + y + z
  • x + y + xyz = x + y

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