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

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Advance Math

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

1. Imagine a gate that implements the logical implicationoperator. Is this gate a Universal Gate (i.e. can any arbitrarycombinational function be implemented if you had an infinite supplyof gates that implement the logical implication operator)? If itis, write the expressions for NOT and OR, ? x and x|y in terms ofthis implication operator. In your expressions, use the charactersequence -> to represent this operator, i.e. x ? y is repesentedin plain text by x -> y.

2. Simplify the following boolean logic expressions that makeuse of the logical implication operator ? into simplest possibleexpressions that you can (in terms of the constants 0 and 1, andthe variables present in the given expressions), while only makinguse of the three standard boolean logic operators ?, & and|.

• (a ? b)&(a ?? b)

• (a ? b)|(b ? c)

• (a|b) ? (a&b)

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