If `AnnB=B ,` then a.`AsubeB` b. `BsubeA` c. `A=varphi` d. `B=varphi`

If A and B are two events such that P(A)!=0 and P(B | A) = 1 ; then(A) AsubB (B) BsubA (C) B=varphi (D) A=varphi

If A and B are two events such that A!=varphi,\ B=varphi, then a. P(A//B)=(P(AnnB))/(P(B)) b. P(A//B)=P(A)P(B) c. P(A//B)=P(B//A)=1 d. P(A//B)=(P(A))/(P(b))

In each of the Exercises choose the correct answer:If A and B are events such that P(A|B) = P(B|A), then (a) AsubB but A!=B (b) A = B (c) AnnB=varphi (d) P (A) = P(B)

O A ,O Ba n dO C ,w i t hO as the origin, are three mutually perpendicular lines whose direction cosines are l_rm_ra n dn_r(r=1,2a n d3)dot If the projection of O Aa n dO B on the plane z=0 make angles varphi_1a n dvarphi_2, respectively, with the x-axis, prove that tan(varphi_1-varphi_2)=+-n_3//n_1n_2dot

For any two sets A and B Ann(AuuB)= a. B b. A c. varphi d. none of these

For any two sets A and B, Ann(AuuB ') is equal to a. A b. B c. varphi d. AnnB

Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly two points of continuity then the value of b are (0,3] b. [0,1] c. (0,2] d. varphi

Let A={a , b ,{c , d},\ e} . Which of the following statements are false and why? (i) {a , b , e} in A (ii) {a , b , c}subA (iii) varphi in A (iv) {varphi}subA

A relation varphi from C\ to\ R is defined by xvarphiyhArr|x|=ydot Which one is correct? a. (2+3i)varphi13 b. 3varphi(-3) c. (1+i)varphi2 d. ivarphi1

Find sets A, B and C such that A nnB , B nnC and A nnC are nonempty sets and A nnB nnC=varphi .