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(a) A function F(A,B,C,D) = Σ m(0, 5, 10, 11, 12, 13, 14). If the minimized Sum of Products (SOP) expression of the function is B.C+A.C+A.C.D, find the obvious don't care entries. (b) Implement a 2-input AND function using 2-to-4 line active low output decoder and a NOT gate. (c) (d) (e) Implement a 4-input Exclusive-NOR gate ABOCOD using minimum number of 2-input Exclusive-OR gates only. (i) A.B+A.B=1 [3 marks] [CO1, PO1, C3] Using Boolean algebra, prove if the following equations are true or not. A.B+B.A = A.B.B.A (iii) Ā.C+A.B=Ā.C+AB+B.C [3 marks] [CO1, PO1, C3] 2 [4 marks] [CO1, PO1, C3] [2 marks] [C01, PO1, C3] [2 marks] [CO1, PO1, C3] [2 marks] [CO1, PO1, C3] Show how a NOT function can be implement with each of the following gates; 3-input NAND gate and 2-input Exclusive-NOR gate. [4 marks] [CO1, PO1, C3]