The stress-strain graphs for materials $A$ and $B$ are shown in the figure. The graphs are drawn to the same scale.
$(a)$ Which of the materials has the greater Young's modulus?
$(b)$ Which of the two is the stronger material?

(A) ; $(b)$ $A$
For a given strain,the stress for material $A$ is greater than it is for material $B$,as shown in the two graphs.
Young's modulus $= \frac{\text{stress}}{\text{strain}}$
For a given strain,if the stress for a material is higher,then Young's modulus is also greater for that material. Therefore,Young's modulus for material $A$ is greater than it is for material $B$.
The strength of a material is determined by the amount of stress required to fracture it,which corresponds to its fracture point. The fracture point is the extreme point in a stress-strain curve. By observing the graphs,the stress at the fracture point for material $A$ is higher than that for material $B$.
Hence,material $A$ is stronger than material $B$.