Define subjective, injective, and bijective functions with the examples.
In mathematics, especially for chemists dealing with quantitative relationships, functions describe how one set of values maps to another. A subjective function (or surjective) is one in which every element ________ __________ ________ ___ ________ _________ ________.
________ _______ _______ __________ __________.
________ ______ ____ _______ _____ ________ _______ ____ _________ _______.
_____ __________ _________ ___ ______.
_______ _______ _______ _____ _________.
___ _______ __________ __________ __________ _______ _______ ___ _____ ____ __________.
__________ ___ _______ ______ __________ ___ _____ _________ ___ ___ ___.
__________ ___ __________ _______ ________ _________ ___ _________ ______.
_______ _____ ____ _______ _________ _______ ___ _______ ______.
_______ __________ _______ ____ _______.
________ ___ _______ ____ _____ __________ _____ ________ _____ ________ _________ __________.
_____ ___ ________ ______ _______ ____ _______ ______ _______ ____.
_____ _____ ______ _______ __________ ____.
____ ___ ______ _______ __________ __________ __________ ___ _________ _____.
_________ __________ ______ __________ ________ __________ ________ _____ ________.
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A number is chosen at random from the first 40 natural numbers. Calculate the probability that the selected is divisible by 5 or 7.
(a) If A = 
then show that
(i) 1/2 (A + A') is symmetric, and
(ii) 1/2 (A - A') is skew symmetric.
∫₁³ x²eˣ³ dx
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√(d³y/dx³) = dy/dx + x⁴
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