Instead of memorizing all four options separately, fix one master relationship first and then algebraically check whether each option is a valid rearrangement of it.
The disaster risk community defines risk with this relationship:
\[ R = \frac{H \times V \times E}{C} \]
where $R$ is risk, $H$ is hazard, $V$ is vulnerability, $E$ is exposure and $C$ is coping capacity. Capacity sits in the denominator because a community that copes well faces less risk for the same hazard, not more.
- (A) $R = H \times V \times E \times C$: here $C$ has been moved from the denominator to the numerator. That flips its effect, making higher capacity increase risk, which contradicts the definition of capacity. Wrong.
- (B) $H = R \times C \times E$: solve the master formula for $H$ properly: $H = \dfrac{R \times C}{V \times E}$. The option drops $V$ from the denominator and instead multiplies by $E$, so it does not match. Wrong.
- (C) $R = \dfrac{H \times V \times E}{C}$: this is the master formula itself, unchanged. Correct.
- (D) $E = \dfrac{H \times V}{R}$: solve the master formula for $E$ properly: $E = \dfrac{R \times C}{H \times V}$. The option has $R$ in the wrong place and $C$ missing entirely, so it does not match. Wrong.
Checking each option as an algebraic rearrangement of the same master formula confirms that only option (C) is consistent.
Let's summarize:
- Master relationship: $R = \dfrac{H \times V \times E}{C}$, with capacity always in the denominator.
- Any option that multiplies capacity into the numerator, or drops a factor while rearranging, breaks the relationship.
So the only correct relationship is option (C).