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Let \( A = \{-2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4\} \). Let \( R \) be a relation on \( A \) defined by \( xRy \) if and only if \( 2x + y \leq 2 \). Let \( l \) be the number of elements in \( R \). Let \( m \) and \( n \) be the minimum number of elements required to be added in \( R \) to make it reflexive and symmetric relations respectively. Then \( l + m + n \) is equal to:

The number of relations, defined on the set \( \{a,b,c,d\} \), which are both reflexive and symmetric, is equal to:

What does the shaded portion of the Venn diagram given below represent?

If the difference between the number of subsets of the sets \( A \) and \( B \) is \( 120 \), then choose the INCORRECT option.

Let \( A=\{1,4,7\} \) and \( B=\{2,3,8\} \). Then the number of elements, in the relation \( R=\{((a_{1},b_{1}),(a_{2},b_{2}))\in(A\times B)\times(A\times B):a_{1}+b_{2}\text{ divides }a_{2}+b_{1}\} \) is ______________ .

Let \( A=\{0,1,2,\ldots,9\} \). Let \( R \) be a relation on \( A \) defined by \( (x,y)\in R \) if and only if \( |x-y| \) is a multiple of \( 3 \).
Given below are two statements:
Statement I: \( n(R)=36 \).
Statement II: \( R \) is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below:

Let \( A = \{2,3,5,7,9\} \). Let \( R \) be the relation on \( A \) defined by \( xRy \) if and only if \( 2x \le 3y \). Let \( l \) be the number of elements in \( R \), and \( m \) be the minimum number of elements required to be added in \( R \) to make it a symmetric relation. Then \( l + m \) is equal to:

Let \( A = \{2, 3, 4, 5, 6\} \). Let \( R \) be a relation on the set \( A \times A \) given by \( (x,y)R(z,w) \) if and only if \( x \) divides \( z \) and \( y \leq w \). Then the number of elements in \( R \) is ________.