Observe the following statements :(I) In $\Delta ABC, b \; \cos ^2 \large\frac{C}{2}+c \cos ^2 \large\frac{B}{2} =s$ (II) In $\Delta ABC, \cot \large\frac{A}{2}=\frac{b+c}{2}$$ => B =90^{\circ}$ Which of the following is correct?

Question

(1) Both I and II a true

(2) I is true, II is false

(3) I is false, II is true

(4) Both I and II are false