A Boolean function x’y’ + xy + x’y is equivalent to
Explanation
1. Diya gaya Expression:
F = x’y’ + xy + x’y
2. Terms ko Rearrange karna:
Hum un terms ko ek saath likhenge jinme common variables hain (jaise x′):
F = (x’y’ + x’y) + xy
3. Common term (x′) ko bahar nikalna (Distributive Law):
F = x'(y’ + y) + xy
4. Complement Law ka upyog:
Hume pata hai ki kisi variable aur uske complement ka sum 1 hota hai:
Ab ise equation mein rakhte hain:
5. Redundancy Law (ya Absorption Law ka extension) ka upyog:
Boolean algebra ka ek mahatvapurna rule hai: A+A′B=A+B.
Yahan A=x′ aur B=y hai.
