Consider the following premises. If Mary plays squash, then Patricia is running. Jennifer is playing tennis if and only if Mary is playing squash. If Patricia goes running, then Jennifer is playing tennis. Can we infer the following from them? If is not true that Mary is playing squash if and only if Patricia is running.
 From the fact that Jennifer is playing tennis if and only if Mary is playing squash we can infer that if Jennifer plays tennis, then Mary is playing squash. From the fact that if Patricia goes running, then Jennifer is playing tennis, and that if Jennifer plays tennis, then Mary is playing squash we can infer that if Patricia goes running, then Mary is playing squash. Finally, from the fact that if Mary plays squash, then Patricia is running, and that if Patricia goes running, then Mary is playing squash we can infer that Mary is playing squash if and only if Patricia is running, which contradicts that If is not true that Mary is playing squash if and only if Patricia is running. Therefore, the answer is no.