GATE Computer Science (CS) 2019 Solved Papers

Question : 16 of 65

Marks: +1, -0

Which one of the following is NOT a valid identity?

Solution:

(a)

x ⊕ y=(x y+x^{'} y^{'})^{'}

=( {xy})^{'}

=x ⊕ y

, it is valid.

(x+y) ⊕ z=(\ov{x+y}) z+(x+y) \ov{z}

(b)

=\ov{ {xy}} {z}+ {x} \ov{ {z}}+ {yz}

1 4,6 2,6

=Σ {m}(1,2,4,6)

x ⊕(y+z)=x(y+z)+x(y+z)

=x y+x z+y z

2,31,34

=∑ {m}(1,2,3,4)

( {x}+ {y}) ⊕ {z} ≠ {x} ⊕( {y}+ {z})

So option (b) is invalid.
(c)

( {x} ⊕ {y}) ⊕ {z}= {x} ⊕( {y} ⊕ {z})

Associativity is true on Ex-OR operator so it valid.
(d)

x ⊕ y=(x+y)(\ov{x}+\ov{y})

=(x+y) \ov{x y}

=( {x}+ {y}) \ov{0}

=( {x}+ {y})

, so it is valid.

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