Answer
(a) TRUE; 2x + y =7 .
(B) THE GIVEN STATEMENT IS TRUE
(C) ALSO THE THIRD STATEMENT IS TRUE
(D) CLEARY THE EQUATION HOLDS.
(E) THIS STATEMENT IS FALSE FOR BOTH X AND Y.
Work Step by Step
(a) TRUE; 2x + y =7 .
GIVE ANY VALUE TO X THERE EXISTS A VALUE OF Y SO THAT GIVEN EQUATION HOLDS.
(B) THE GIVEN STATEMENT IS TRUE
(C) ALSO THE THIRD STATEMENT IS TRUE FOR BOTH X AND Y.GIVEN ANY VALUE TO X, THE SAME VALUE FOR Y SATISFIES THE GIVEN EQUATION
(D) CLEARY THE EQUATION HOLDS. GIVE ANY VALUE TO X THERE EXISTS A VALUE OF Y=1 WHICH SATISFIES THE GIVEN EQUATION.SIMILARLY, GIVE ANY VALUE TOY THERE EXISTS A VALUE OF X=5 WHICH SATISFIES THE GIVEN EQUATION
(E) THIS STATEMENT IS FALSE FOR BOTH X AND Y.
BECAUSE IF WE GIVE ANY VALUE TO X THERE EXISTS AN IMAGINARY VALUE OF Y WHICH SATISFIES THE GIVEN EQUATION. THUS THERE DOES NOT EXIST A REAL NO.
