Given the Boolean functions F1 and F2, show that. a) The Boolean function E = F1...

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Given the Boolean functions F1 and F2, show that. a) The Boolean function E = F1 + F2 contains the sum of min terms of F1 and F2. b) The Boolean function G = F1F2 contains only the min terms that are common to F1 andF2. I showed one example of these facts using a truth table of some function as such: A F₁ 0 0 1 0 1 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 1 0 1 0 1 Clearly shown is: F1 = M1 + m3 +m5 + m7 F2 = mo + m1 +m4 + ms and F2 1 1 0 0 1 1 0 0 F1+F2= mo +m1 + m3 + m4 + m5 +m7 and F1+F2 1 1 0 1 1 1 0 1 F1F2 1 1 0 1 1 1 0 1 F₁F2 = M1 +m5 These support the statements shown, but are not proofs there of because they are only an example. How would one prove this? Given the Boolean functions F1 and F2, show that. a) The Boolean function E = F1 + F2 contains the sum of min terms of F1 and F2. b) The Boolean function G = F1F2 contains only the min terms that are common to F1 andF2. I showed one example of these facts using a truth table of some function as such: A F₁ 0 0 1 0 1 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 1 0 1 0 1 Clearly shown is: F1 = M1 + m3 +m5 + m7 F2 = mo + m1 +m4 + ms and F2 1 1 0 0 1 1 0 0 F1+F2= mo +m1 + m3 + m4 + m5 +m7 and F1+F2 1 1 0 1 1 1 0 1 F1F2 1 1 0 1 1 1 0 1 F₁F2 = M1 +m5 These support the statements shown, but are not proofs there of because they are only an example. How would one prove this?