answer questions

1. From a group of students surveyed, it is determined that 28 students like Chinese food, 23 students like Italian food and 35 students like Mexican food. A total of 15 students like Chinese and Italian food, 20 students like Chinese and Mexican food and 12 students like Italian and Mexican food. A total of 9 students like all 3. (a) How many students like at least one of Chinese, Italian and Mexican food? (b) How many students like exactly two of Chinese, Italian and Mexican food? 2. Consider the cryptosystem in which the integer x associated with a letter is transformed into f(x) = 3x mod 26. In this case, decryption is defined by f-(x) = 9x mod 26. (a) Into which secret word is the word GUM transformed? (b) Which word is transformed into the secret word FOYN? (c) Which word is transformed into the secret word JAN