Q. 1 Maximum score 15 Test the validity of the following arguments: If I work, I cannot study, Either I study, or I pass CSC 1500 I worked Therefore, I passed CSC 1500. (Hint: Translate the argument into symbolic form, by letting p be "I work" with a symbol and like wise other relevant phrases. Then write three prepositions (premises) before the dotted line and the conclusion (after the dotted line) into symbolic form. Construct the appropriate truth tables (for three premises and the conclusion). The argument is valid if the conclusion is true whenever all the premises are true; otherwise the argument is false.) Note: Please be advised that you should do this homework and others on your own. Any evidence of plagiarism will be severally dealt with. Q.2. Maximum score 20 (5 per part) (a) Express the number (01110110)2 (a number in binary system or base 2, into base 10 (decimal). (b) Express the number (67) 10 (a number in decimal system or base 10) into base 2 (binary). (c) Execute the following operations with the binary numbers given and check your results by converting each of the numbers to their decimal (base 10) equivalents. 101011 +111111 +111011 +010101 (d) 1111 x 1010 Q. 3 Maximum score 15 You receive the following binary message: 1011001. The message includes three check bits. (a) Which bit was erroneously received? (b) What was the correct number (in decimal system) sent