1) abcD+abcd+aBCd+aBCD
then the simplified function is
( Capital letters are copliments of corresponding letters A=compliment of a)
[a] a ab [c] abc [d] a(bc)* [e] none
(bc)*=compliment of bc

• abcD + abcd + aBCd + aBCD
  = abc(D + d) + aBC(d + D)
  = abc + aBC because d + D = 1 , D being complement of d
  = a(bc + BC)
  = a because bc + BC = 1, BC being complement of bc
  
• 12 years agoHelpfull: Yes(21) No(1)
• abcD+abcd+aBCd+aBCD
  abc(D+d)+aBC(d+D)
  abc(1)+aBC(1)
  a(bc+BC)
  a(1)=a
  
• 12 years agoHelpfull: Yes(7) No(3)
• abcD + abcd + aBCd + aBCD
  = abc(D + d) + aBC(d + D)
  = abc + aBC
  = a (bc + BC)
  = a (b XNOR c)
  So, answer is option(e) none
  
• 12 years agoHelpfull: Yes(7) No(3)