State whether the following statements are true or false. Justify your

Question

State whether the following statements are true or false. Justify your answer with a short explanation or a counter-example. (2 × 10 = 20)
(i) The contra- positive of the statement $"x^2+y^2=0\Rightarrow x=0$ and $y=o"$ is $"x\neq 0$ and $"y\neq 0\Rightarrow x^2+y^2\neq 0"."$
(ii) $a^n=\frac{1}{9}[2^{n+1}+(-1)^n]^2$ is the solution of the recurrence relation
$\sqrt{a_n}=\sqrt{a_{n-1}}+2\sqrt{a_{n-2}},(n\geq 1),a_0=a_1=1.$
(iii) The number of integers between 1 and 360 which are relatively prime to 360 are
96.[ Note that 1 is relatively prime to every positive integer.]
(iv) The coefficient of $x^6y^5z^9$ in $(x+y+z)^{20}$ is $C(20,6).C(20,5).C(20,9).$
(v) If a graph has 6 vertices and 10 edges, then it can’t be regular.
(vi) Peterson graph is bipartite.
(vii) Every edge of a Tree is a bridge.
(viii) The independence number of $C_5,i.e.,\alpha (C_5)$ is $2.$
(ix) The DNF of the expression $p(x,y,z)=(x\wedge z)^{'}$ is $(x\vee y\,\vee z^{'})\vee(x\,\vee\,y^{'}\vee\,z^{'}).$
(x) The number 8 has atmost one self-conjugate partition.

12 Mar 2024

Answer :

Word Count : 318

(i) True: The contrapositive of a conditional statement switches the hypothesis and conclusion while negating both. The statement "x^2+y^2=0\Rightarrow x=0 and y=0" implies that if the sum of the squares of two numbers is zero, then both numbers must be zero. The contrapositive of this statement is indeed "x≠0 and y≠0⇒x^2+y^2≠0", which asserts that if neither x nor y is zero, then their _____ __________ ________ ____ _______ ___ _____.
______ _________ __________ __________ __________ __________ __________.
_______ _____ ______ ___ __________ ____ ___ ________ ___.
___ ______ _________ ___ __________ _________ ________ __________ _______ __________ ______.
_____ ___ _______ ______ ______ _____ __________ ________ _______.
______ _______ _____ __________ _________ _____.
________ ______ _____ ___ _________.
_________ ___ _______ _______ ______ ______ __________ ________ _______ ___ ___.
___ _____ _______ ___ ___ ____ _________ ________ _________.
_______ ____ ______ _______ _________ _________ ______ _____ _____ _________ ___ __________.
_____ ____ ___ _______ ___ _______ _______ __________ ________ _______ ___ ______.
________ ____ _____ _________ ___ ________ _____ ________ ________ ______ ___.
________ _____ ________ __________ _________ ____ ________ _____ ______ _______ ___ ___.
______ ____ _________ ___ __________ __________ _________ ______ ________.
____ __________ __________ ___ ____.
_________ __________ _______ _________ ___ _________ ________.
_________ ____ ____ _________ __________ ________ _____.
_________ ___ ____ ___ _______.
________ ___ __________ _______ _____.
__________ _______ _______ ____ _____.
____ _____ ____ _____ _________ _____ _____.
_____ _______ ___ _______ _________ ____ ________ ______ __________ ___.
_________ ____ _______ ___ _________ _________ __________ _________ ___.
_________ ____ _____ __________ _______ _________ ________ _______ __________.
_______ ___ ______ _______ _____ ___ _________ ______ _______ _________ ________.
________ ____ _____ _____ __________ _______ ________ ____ ____ ____ ____ _________.
________ __________ ______ ________ _______ ____ _______ ______ ________.
_______ ___ ____ _______ ____ __________ ________ ______ ________ _____ _______ __________.
______ ____ ________ _________ _________ _________.
_____ ______ ______ _______ ____ _________.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★