To solve this question, the user needs to understand logical connectives and how to interpret compound statements.
The statement "Shelly likes Mike and she likes John" is a compound statement that consists of two individual statements connected by the logical connective "and." The truth value of this compound statement depends on the truth values of its individual statements.
Since the question states that Shelly does not like John, the individual statement "Shelly likes John" is false. Therefore, the overall truth value of the compound statement is false, regardless of whether the statement "Shelly likes Mike" is true or false.
Now, let's go through each option:
A. True: This option is incorrect because the compound statement is false.
B. False: This option is correct. As explained above, the compound statement is false due to the falsehood of the individual statement "Shelly likes John."
C. Shelly likes Peter: This option is not relevant to the given statement.
D. none of the above: This option is incorrect because option B is the correct answer.
Therefore, The Answer is: B. False.