Let `A={a , b , c , d},\ B={a , b , c}a n d\ C={b , d}` . Find all sets `X` such that: `XsubA\ a n d\ Xsub Bdot`

Let A={a , b , c , d},\ B={a , b , c}a n d\ C={b , d} . Find all sets X such that: XsubB\ a n d\ XsubCdot

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .

In A B C ,\ /_A=100^0a n d\ A B=A Cdot Find /_B\ a n d\ /_C

Let R be a relation on NxxN defined by (a , b)\ R(c , d)hArra+d=b+c\ if\ (a , b),(c , d) in NxxN then show that: (i)\ (a , b)R\ (a , b)\ for\ a l l\ (a , b) in NxxN (ii)\ (a , b)R(c , d)=>(c , d)R(a , b)for\ a l l\ (a , b),\ (c , d) in NxxN (iii)\ (a , b)R\ (c , d)a n d\ (c , d)R(e ,f)=>(a , b)R(e ,f)\ for all \ (a , b),\ (c , d),\ (e ,f) in NxxN

Let A={a , b , c , d}a n df: AvecA be given by f={(a , b),(b , d),(c , a),(d , c)}, write f^(-1)dot

Let N be the set of all natural numbers and let R be a relation on NxxN , defined by (a ,\ b)R\ (c ,\ d) a d=b c for all (a ,\ b),\ (c ,\ d) in NxxN . Show that R is an equivalence relation on NxxN

In the adjoining figure A B D C\ a n d\ D A is perpendicular to A Bdot Further, D C=7c m ,\ C B=10 c m\ a n d\ A B=13 c mdot Find the area of the quadrilateral A B C Ddot

In Figure, A C > A B\ a n d\ D is the point on A C such that A B=A Ddot Prove that B C > C D