Events E and F are such that P(not E or not F) = 0.25,

It is given that P (not E or not F) = 0.25

i.e., $P\left(E^{\prime} \cup F^{\prime}\right)=0.25$

$\Rightarrow \mathrm{P}(\mathrm{E} \cap \mathrm{F})^{\prime}=0.25 \quad\left[\mathrm{E}^{\prime} \cup \mathrm{F}^{\prime}=(\mathrm{E} \cap \mathrm{F})^{\prime}\right]$

Now, $P(E \cap F)=1-P(E \cap F)^{\prime}$

$\Rightarrow P(E \cap F)=1-0.25$

$\Rightarrow P(E \cap F)=0.75 \neq 0$

$\Rightarrow \mathrm{E} \cap \mathrm{F} \neq \phi$

Thus, E and F are not mutually exclusive.