JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Importance and Snapshot of Principle of Mathematical Induction - Study ref# 611

Introduction:
Inductive reasoning depends on working with each case, and
developing a conjecture by observing the incidences till we observe each and
every case. Thus in simple words, the induction means the generalization from
particu... read more

JEE-Main - Grade 11 - Mathematics - Mathematical Reasoning - Importance and Snapshot of Mathematical Reasoning - Study ref# 641

Introduction
In this Chapter, we shall discuss about some basic ideas
of Mathematical Reasoning. All of us know that human beings evolved from the
lower species over many millennia. The main asset that made humans “superior”
to other spec... read more

JEE-Main - Grade 11 - Mathematics - Mathematical Reasoning - Importance and Snapshot of Mathematical Reasoning - Study ref# 642

Following sections must be covered to understand the
Mathematical Reasoning:
1. Statements
2. New Statements from Old
3. Implications
4. Validating Statements... read more

JEE-Main - Grade 11 - Mathematics - Mathematical Reasoning - Target Setup for Mathematical Reasoning - Study ref# 643

Student requires to achieve the following milestones to get better grip over Mathematical Reasoning. The milestones / targets are as follows:-Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test0... read more

Which of the following sentences are statements? Give
reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.... read more

Are the following pairs of statements negations of each
other:
(i) The number x is not a rational number.
The number x is not an
irrational number.
(ii) The number x is a
rational number.
The number x is an irration... read more

Find the component statements of the following compound
statements and check whether they are true or false.
(i) Number 3 is prime or it is odd.
(ii) All integers are positive or negative.
(iii) 100 is divisible by 3, 11 and 5. Answer: (i... read more

For each of the following compound statements first
identify connecting words and then break it into component statements:
(i) All rational numbers are real and all real numbers are
not complex.
(ii) Square of an integer is positive or... read more

Rewrite the following with ‘if-then’ in five different
ways conveying the same meaning:
If a natural number is odd, then its square is also odd. Answer: (i) A natural number is odd implies that its square is
odd.
(ii) A natural number ... read more

Show that the statement
p: ‘If x is a real number such that , then x
is 0’ is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive. Answer: (i) Direct method
(ii) Method of contradictio... read more

Show that the following is true by the method of
contrapositive
p: If x is an integer and is even, then
x is also even. Answer: Let x is not even i.e., x = 2n + 1
x2 = (2n+1)2 = 4n2 + 4n
+1
= 4(n2 + n) + 1
4(x2 + x) +1 ... read more

State the converse and contrapositive of each of the following
statements:
(i) p: A positive integer is prime only if it has no
divisors other than 1 and itself.
(ii) q: I go to beach whenever it is a sunny day.
(iii) r: I... read more

Rewrite each of the following statements in the form ‘p’
if and only if ‘q’.
(i) p: if you watch television, then your mind is free and
if your mind is free, then you watch television.
(ii) q: For you to get an A grade, if it is nec... read more

Form the biconditional statements p q, where
(i) p: The unit digit of an integer is zero.
q: It is divisible by 5.
(ii) p: The natural number n is odd.
q: Natura... read more

Blog - Benefits of Taking SAT Practice Tests and How They Enhance Your Mental Capabilities

How SAT Practice Tests enhance your mental capabilitiesTaking mock SAT test helps in building your cognitive abilities. You can also get a better hold of time management and brush your various skills in reasoning. It enhances your vocabulary and math...