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={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=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.

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , prove that: a : b = c : d .

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

In Figure, A B C\ a n d\ D B C are two isosceles triangles on the same base B C such that A B=A C\ a n d\ D B=C Ddot Prove that /_A B D=\ /_A C D

In Figure, A D=A E\ a n d\ D\ a n d\ E are points on B C such that B D=E Cdot Prove that A B=A C