The negation of the Boolean expression \(x\leftrightarrow\ \sim y\) is equivalent to :
Show Hint
- \((x\wedge y)\vee(\sim x\wedge\ \sim y)\)
- \((\sim x\wedge y)\vee(\sim x\wedge\ \sim y)\)
- \((x\wedge y)\wedge(\sim x\vee\ \sim y)\)
- \((x\wedge\ \sim y)\vee(\sim x\wedge y)\)
The Correct Option is A
Solution and Explanation
Negation: \(\sim[(x\wedge\ \sim y)\vee(\sim x\wedge y)]\equiv(\sim x\vee y)\wedge(x\vee\ \sim y)\).
Expand: \((\sim x\wedge x)\vee(\sim x\wedge\ \sim y)\vee(y\wedge x)\vee(y\wedge\ \sim y)\equiv(\sim x\wedge\ \sim y)\vee(x\wedge y)\).
This is option (1).
Answer: (1) \((x\wedge y)\vee(\sim x\wedge\ \sim y)\)
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