Final answer:
The statement is true; mice injected with a mixture of heat-killed S strain and live R strain did die, as discovered in Griffith's transformation experiments.
Step-by-step explanation:
The statement that mice injected with a mixture of bacteria from heat-killed smooth (S) colonies and live rough (R) colonies died is true. This finding was part of the groundbreaking work by Frederick Griffith, which is known as Griffith's transformation experiments. These experiments were pivotal in demonstrating that there was a 'transforming principle' responsible for transferring genetic information. This was later understood to be the DNA. When Griffith injected the live R strain alone or heat-killed S strain alone into mice, they survived. However, when mice were injected with a combination of heat-killed S strain and live R strain, the mice died. Upon examination, it was found that only the S strain, which is the virulent form, was recovered from the dead mice. This implied that the heat-killed S strain somehow transformed the nonpathogenic R strain into a pathogenic form.