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Simplify Y = AB’ + (A’ + B)C
- a)AB’ + C
- b)AB + AC
- c)A’B + AC’
- d)AB + A
Correct answer is option 'A'. Can you explain this answer?
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Simplify Y = AB’ + (A’ + B)Ca)AB’ + Cb)AB + ACc)A&rs...
Y = AB’ + (A’ + B)C = AB’ + (A’ + B)C = AB’ + (AB’)’C = AB’ + C.
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Simplify Y = AB’ + (A’ + B)Ca)AB’ + Cb)AB + ACc)A&rs...
Option verificationPut A,B,C all without dash(')=1 And A',B',C' all with dash(')=0After verification option A only satisfies
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Simplify Y = AB’ + (A’ + B)Ca)AB’ + Cb)AB + ACc)A&rs...
Understanding the Expression
To simplify the expression Y = AB' + (A' + B)C, we need to break it down step by step.
Step 1: Distribute C
- The term (A' + B)C can be expanded using the distributive property:
(A' + B)C = A'C + BC
- Therefore, the equation becomes:
Y = AB' + A'C + BC
Step 2: Look for Common Terms
- The expression now is:
Y = AB' + A'C + BC
- We will analyze if we can combine or simplify the terms further.
Step 3: Apply Consensus Theorem
- The Consensus Theorem states that AB + A'C + BC = AB + A'C.
- However, we notice that the term AB' does not have a direct counterpart to form a consensus with A'C and BC.
Step 4: Identify Redundant Terms
- The presence of C in A'C and BC suggests we may not need both if A'C can cover cases where C is true.
- If we inspect AB' + A'C, we see that if A is true and B is false, AB' is true, and if A is false, A'C is true.
Final Simplification
- Therefore, the expression can be simplified to:
Y = AB' + C
- This means option 'A' is correct.
Conclusion
- The simplified form of the original expression is indeed:
Y = AB' + C.
To simplify the expression Y = AB' + (A' + B)C, we need to break it down step by step.
Step 1: Distribute C
- The term (A' + B)C can be expanded using the distributive property:
(A' + B)C = A'C + BC
- Therefore, the equation becomes:
Y = AB' + A'C + BC
Step 2: Look for Common Terms
- The expression now is:
Y = AB' + A'C + BC
- We will analyze if we can combine or simplify the terms further.
Step 3: Apply Consensus Theorem
- The Consensus Theorem states that AB + A'C + BC = AB + A'C.
- However, we notice that the term AB' does not have a direct counterpart to form a consensus with A'C and BC.
Step 4: Identify Redundant Terms
- The presence of C in A'C and BC suggests we may not need both if A'C can cover cases where C is true.
- If we inspect AB' + A'C, we see that if A is true and B is false, AB' is true, and if A is false, A'C is true.
Final Simplification
- Therefore, the expression can be simplified to:
Y = AB' + C
- This means option 'A' is correct.
Conclusion
- The simplified form of the original expression is indeed:
Y = AB' + C.
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Simplify Y = AB’ + (A’ + B)Ca)AB’ + Cb)AB + ACc)A’B + AC’d)AB + ACorrect answer is option 'A'. Can you explain this answer?
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