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A function of Boolean variables $X, Y$ and $Z$ is expressed in terms of the min-terms as $$F(X, Y, Z) = \Sigma (1, 2, 5, 6, 7)$$

Which one of the product of sums given below is equal to the function $F(X, Y, Z)?$

  1. $(\overline{X} + \overline{Y} + \overline{Z} )\cdot(\overline{X} + Y + Z)\cdot(X + \overline{Y} + \overline{Z} )$
  2. $(X + Y + Z)\cdot(X + \overline{Y} + \overline{Z} )\cdot(\overline{X} + Y + Z)$
  3. $(\overline{X} + \overline{Y} + Z)\cdot(\overline{X} + Y + \overline{Z} )\cdot(X + \overline{Y} + Z)\cdot(X + Y + \overline{Z} )\cdot(X + Y + Z)$
  4. $(X + Y + \overline{Z} )\cdot(\overline{X} + Y + Z)\cdot(\overline{X} + Y + \overline{Z} )\cdot(\overline{X} + \overline{Y} + Z)\cdot(\overline{X} + \overline{Y} + \overline{Z})$
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