Question

प्रश्न-3 अनुच्छेदर्म ्पठित्वा प्रश्नान्उत्तरत- (गदयांश को पढ़कर प्रश्नों के उत्तर दीब्िए-)

तदा कब्श्चत्पधथक: तत्र आगच्छत्। साः तान्बािकान्दु:णखतान्दृष््वा अपृच्छत्-बािकााः!

युष्र्माकं दुाःखस्य कारर्ं ककर्म ्? बािकानां नायकाः अकथयत्- वय दश बािकााः स्नातुर्म ्

आगता:। इदानीं नव एव स्र्म:। एक: नदयां र्मग्न: इतत।

एकपदेन उत्तरत- (एक पद र्मे उत्तर दीब्िए)

क) तत्र क: आगच्छत्?

ख) कतत बािका: आसन्?

पूर्णवाक्येन उत्तरत- (पूर्ण वाक्य र्मे उत्तर दीब्िए)

क) पधथक: बािकान्ककर्म ्अपृच्छत्?

तनदेशानुसार: उत्तरत- ( तनदेशानुसार उत्तर दीब्िए)

क) अनुच्छेद से दो अव्यय छााँटकर लिखें –​

Answer 1

Answer:

Antisymmetric Relation Examples

Q.1: Which of these are antisymmetric?

(i) R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,1),(4,4)}

(ii) R = {(1,1),(1,3),(3,1)}

(iii) R = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)}

Solution:

(i) R is not antisymmetric here because of (1,2) ∈ R and (2,1) ∈ R, but 1 ≠ 2.

(ii) R is not antisymmetric here because of (1,3) ∈ R and (3,1) ∈ R, but 1 ≠ 3.

(iii) R is not antisymmetric here because of (1,2) ∈ R and (2,1) ∈ R, but 1 ≠ 2 and also (1,4) ∈ R and (4,1) ∈ R but 1 ≠ 4.

Answer 2

Answer:

Antisymmetric Relation Examples

Q.1: Which of these are antisymmetric?

(i) R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,1),(4,4)}

(ii) R = {(1,1),(1,3),(3,1)}

(iii) R = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)}

Solution:

(i) R is not antisymmetric here because of (1,2) ∈ R and (2,1) ∈ R, but 1 ≠ 2.

(ii) R is not antisymmetric here because of (1,3) ∈ R and (3,1) ∈ R, but 1 ≠ 3.

(iii) R is not antisymmetric here because of (1,2) ∈ R and (2,1) ∈ R, but 1 ≠ 2 and also (1,4) ∈ R and (4,1) ∈ R but 1 ≠ 4.