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In: Advanced Math

An operation called the logical implication, is written as x → y and corresponds to English...

An operation called the logical implication, is written as x → y and corresponds to English statements “x implies y” or “if x then y”. The implication operator outputs 0 if the first operand is 1 and the second operand is 0, and outputs 1 otherwise.

1. Imagine a gate that implements the logical implication operator. Is this gate a Universal Gate (i.e. can any arbitrary combinational function be implemented if you had an infinite supply of gates that implement the logical implication operator)? If it is, write the expressions for NOT and OR, ∼ x and x|y in terms of this implication operator. In your expressions, use the character sequence -> to represent this operator, i.e. x → y is repesented in plain text by x -> y.

2. Simplify the following boolean logic expressions that make use of the logical implication operator → into simplest possible expressions that you can (in terms of the constants 0 and 1, and the variables present in the given expressions), while only making use of the three standard boolean logic operators ∼, & and |.

• (a → b)&(a →∼ b)

• (a → b)|(b → c)

• (a|b) → (a&b)

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Expert Solution

Colby Messinger answered 1 year ago
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