Holla user.
have an attention plz
Can anyone tell me all the formulae of "mathematical resoning" with its short summary.
No sparm ans.
Answers
In this article, we provide you a short and effective summary for Percentages. We cover a list of 15 formulas and short-cuts that you can use for Percentage questions. The following is a list of important formulas for Percentage:
1. Percent implies “for every hundred”.
% is read as percentage and x % is read as x per cent.
2. To calculate p % of y
(p/100) x y = (p x y)/100
p % of y = y % of p
3. To find what percentage of x is y: y/x × 100
4. To calculate percentage change in value
Percentage change = {change/(initial value)} x 100
5. Percentage point change = Difference of two percentage figures
6. Increase N by S % = N( 1+ S/100 )
7. Decrease N by S % = N (1 – S/100)
8. If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original point is 100x/ (100 + x) %.
9. If A is x% more /less than B, then B is 100x/(100 + x) % less/more than A.
10. If the price of an item goes up/down by x %, then the quantity consumed should be reduced by 100x/ (100 + x)% so that the total expenditure remains the same.
11. Successive Percentage Change
If there are successive percentage increases of a % and b%, the effective percentage increase is:
{(a + b + (ab/100)}%
Hope it helps!
Laws of Algebra of Statements
(i) Idempotent Laws
(a) p ∨ p ≡ p
(b) p ∧ p ≡ p
(ii) Associative Laws
(a) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
(b) (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
(iii) Commutative Laws
(a) p ∨ q ≡ q ∨ p
(b) p ∧ q ≡ q ∧ P
(iv) Distributive Laws
(a) p ∨ (q A r) ≡ (p ∨ q) ∧ (p ∨ r)
(b) p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
(v) De Morgan’s Laws
(a) ~(p ∨ q) ≡ (~ p) ∧ (,_ q)
(b) ~(p ∧ q) ≡ (~ p) ∨ (~ q)
(vi) Identity Laws
(a) p ∧ F ≡ F
(b) p ∧ T ≡ p
(c) p ∨ T ≡ T
(d) p ∨ F ≡ p
(vii) Complement Laws
(a) p ∨ (~ p) ≡ T
(b) p ∧ (~ p) ≡ F
(c) ~ (~p) ≡ p
(d) ~ T ≡ F, ~ F ≡ T
Important Points to be Remembered
(i) The number of rows of table is depend on the number of statements.
(a) If p is false, then ~ p is true.
(b) If P is true, then ~ p is false.
(ii) (a) The converse of p => q is q => p.
(b) The inverse of p => q is ~ p => ~ q.
(iii) The contrapositive of p => q is ~ q => ~ p.
A statement which is neither a tautology nor a contradiction is a contingency.