A "logical disjunction" simply means : " or " so;
"A ∨ B " is read as "A or B ". Such a disjunction is false if both A and B are false.
So, the result would be true if one or more operands are true.
It would only be false if both or all it's operands are false.
A "logical conjunction" simply means "and" so;
the symbol is an inverted "v"
" A (inverted v) B " are read as " A and B " . The conjunction would only be true if and only if both operands are true, otherwise it would be false.
properties under the conjunctions are:
1. "Associativity": the order of operations does not matter as long as the sequence of the operands is not changed. Eventhough parenthesis are changed, operands will still act the same.
ex: (5+1) +5 = 5+ (1+5)
2. "Commutativity": to the ability to change the order of something without changing the end result.
ex: 3 + 5 = 5 + 3 for addition; 5*3 = 3*5 for multiplication
3. "Distributivity": uses the "dristibutive law"
ex: 5( 2 + 3) = (5*2) + (5*3)
4. "Idempotence": multiple applications of that operation will yield the same result.
- the absolute value operation is a unary operation on the real numbers
- the opposite operation (-x) on the real numbers
- the power operations (squaring, cubing, etc) on the real numbers
- the factorial operation on the real numbers
- the trigonometric functions (sin x, cos x, tan x, cot x, csc x, sec x) on the real numbers
- the natural logarithm (ln x) on the real numbers
- the logarithm of base 10 (log x) on the real numbers
- logical negation on truth values
These are examples of unary operations, and could be subject to "Idempotence"
5. "Monotonic" - actually these are used mostly for calculus..
There's much more to explain, but it would be best if there would be an example for it? have a nice day!