In Boolean algebra which is equal to X+XY+Y ?
And plz explain it
Answers
Answer:
It took a moment for me to understand the notations. I guess it's been longer than I thought, so let's review the notation.
Multiplication represents AND. Suppose FALSE is represented by zero (0) and TRUE is represented by one (1), then the product of two terms (or any number of terms) is non-zero (TRUE) only when every term is non-zero.
Addition represents OR. The only time the result is FALSE (zero) is when all terms are zero. If any term is TRUE (one) then the result is TRUE.
When a term has a bar over it or is primed, followed by a prime mark ('), it is negated. Thus, TRUE' is FALSE and FALSE' is TRUE. This operation is unary (has one operand) and is called NOT. A minus (negative) sign is often used for NOT. Thus both -a and a’ signify NOT a.
Given these notations we can read the expression a'b' + ab as NOT a AND NOT b OR a AND b. Logical operations have the same order of execution as do arithmetic operations. Therefore, negation (-a, a') before multiplication (a*b, ab, a AND b) before addition (a+b, a OR b) . With this information we can ad parentheses. To clarify the order of operation. We rewrite the original expression as ((NOT a) AND (NOT b) OR (a AND b).
To finish up we can see that a'b' is TRUE only when a and b are both FALSE, and ab is TRUE only when a and b are both TRUE. Finally (sigh of relief) , OR is TRUE only when at least one argument is TRUE. In this case the result is TRUE when either both a and b are FALSE or both are TRUE. If memory serves this is called EQUIVALENT, but it is rarely seen. More often we see. Exclusive OR, XOR, which is TRUE only when its arguments are different (only one is TRUE). Thus the original expression can be rewritten as NOT (a OR b) or a EQUIVALENT b.
Answer:
X^Y^
Explanation:
Boolean algebra =X+XY+Y
Boolean algebra= X
XY
+ Y
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Ans X^Y^
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