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Why does the expression (a && b) || (a && !b) simplify to just a in C?

hard📝 Conceptual Q10 of 15
C - Operators and Expressions
Why does the expression (a && b) || (a && !b) simplify to just a in C?
ABecause b cancels out in logical expressions
BBecause a AND (b OR NOT b) is always a
CBecause a is always true
DBecause NOT operator negates a
Step-by-Step Solution
Solution:

  1. Step 1: Analyze the expression

    (a && b) || (a && !b) means a AND b OR a AND NOT b.

  2. Step 2: Apply distributive law

    This equals a AND (b OR NOT b). Since (b OR NOT b) is always true, expression equals a.

  3. Final Answer:

    Because a AND (b OR NOT b) is always a -> Option B

  4. Quick Check:

    Logical tautology simplifies expression [OK]
Quick Trick: b OR NOT b is always true, so expression equals a [OK]
Common Mistakes:
  • Thinking b cancels out
  • Assuming a is always true
  • Misunderstanding NOT operator

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