Logical Equivalence and Duality
Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represented by p ..
Statement:
For all values of q , cos (- q ) = cos q and sin (- q ) = -sin q..
Note:
i) The numerical values of sin q and cos q cannot be greater than 1. ii) The numerical values of sec q and cosec q can never be less than 1. iii) There is no restriction on the values of tan q and cot q..
i) The numerical values of sin q and cos q cannot be greater than 1. ii) The numerical values of sec q and cosec q can never be less than 1. iii) There is no restriction on the values of tan q and cot q..Note:
The equation sec q = 0, cosec q = 0 can have no solutions as the values of sec q and cosec q cannot be numerically less than ..
Reaction Quotient and the Equilibrium Constant
The concentration ratio, i.e., the ratio of the product of concentration of the products to that of the reactants at any time (t) is known as the concentration quotient 'Q' of the reaction at time (t). The value of Q c or Q p will be different from th..
qth roots of a Complex number
To find the q th roots of a Complex number - One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. ..
To find the q th roots of a Complex number - One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. ..Scientific Notation
Notation of large number in terms of exponential form, 10 raised to required value. It is also a standart notation representation as " p x 10 q ". where 'p' and 'q' are any integers..
Polar form of a Complex number
is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z). The value of q is such that - p < q p , is called the principal value of the ..
is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z). The value of q is such that - p < q p , is called the principal value of the ..C3
If p has the truth value F and q has the truth value T, then p q has the truth value T (F T = T). If p has a truth value F and q has the truth value T, then p: is not a prime number q: x 2 is not a prime ..
If p has the truth value F and q has the truth value T, then p q has the truth value T (F T = T). If p has a truth value F and q has the truth value T, then p: is not a prime number q: x 2 is not a prime ..C4
If both p and q have the truth value F, p q has the truth value T(F F = T). It should be noted that in the above example, the simple statement p and q depend on each other. In other words, if the truth value of one depends on the trut..
If both p and q have the truth value F, p q has the truth value T(F F = T). It should be noted that in the above example, the simple statement p and q depend on each other. In other words, if the truth value of one depends on the trut.. Result
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