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What is Deductive Reasoning ?
Geometry is based on a deductive structure -- a system of thought in which conclusions are justified by means of previously assumed or proved statements. The process of deductive reasoning involves three steps:
Step 1: Start with the given conditions (hypothesis).
Step 2: Use logic, definitions, postulates, or previously proved theorems to justify a sequence of thoughts.
Step 3: State your conclusions.
Example 4 : Given DABC is an equilateral triangle with three congruent sides A@B@C. After we use logic to supply the correct statements in step 2, we can come to the conclusion (theorem): If all the three sides of a triangle are congruent, then the three angles are congruent.
A circular disc of 6 cm radius is divided into three sectors with central angles 1200, 1500,900. What part of the circle is the sector with central angles 1200. Also give the ratio
2x+4x
1
Euler''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?
The subsequent topic that we require to take a look at is the determinant of a matrix. The determinant is in fact a function that gets a square matrix and converts this in a number
a, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c are in h.p To prove: (b+c-a)/a; (a+c-b)/b; (a+b-c)/c are in A.P or (b+c)/a; (a+c)/b; (a+b)/c are in A.P or 1/a; 1
how to simplify an expression which has different signs
Let A be an n×n matrix. Then Show that the set U = {u?R^n : Au = -3un} is a Subspace of R^n
A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days. The remaining 2 days may be any of the following : (i) Sunday and Monday (ii) Monday and Tuesday (iii)
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