Q75 / 110 · VITEEE 2023 · Mathematics

Consider the switching circuit Logical expression corresponding to the complimentary to the above circuit is Figure

  • Correct answer
    A
    a.b.c'
  • B
    \(\mathrm{a}+\mathrm{b}+\mathrm{c}^{\prime}\)
  • C
    \(a^{\prime} \cdot b^{\prime} . c\)
  • D
    none

Solution

Logical expression corresponding to above circuit is \(=a^{\prime}+b^{\prime}+c\) Logical expression corresponding to the complimentary to the above circuit is \(\begin{aligned} & \left(a^{\prime}+b^{\prime}+c\right)^{\prime}=\left(a^{\prime}+b^{\prime}\right)^{\prime} \cdot c^{\prime} \\ & =\left(a^{\prime}\right)^{\prime} \cdot\left(b^{\prime}\right)^{\prime} \cdot c^{\prime} \\ & =a \cdot b \cdot c^{\prime} \quad\left[\left(a^{\prime}\right)^{\prime}=a ;\left(b^{\prime}\right)^{\prime}=b\right] \end{aligned}\)

Hence, the correct answer is option: 'A'.

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