Theory question 106
Logic(a) (i) Illustrate the following statement in a Venn diagram: All good Literature students in a school are in the General Arts class. (ii) Use the diagram to determine whether or not the following are valid conclusions from the given statement: I. Vivian is in the General Arts class therefore she is a good Literature student; II. Audu is not a good Literature student therefore he is not in the General Arts class; III. Kweku is not in the General Arts class therefore he is not a good Literature student.
(b) The cost (c) of producing n bricks is the sum of a fixed amount h, and a variable amount y, where y varies directly as n. If it costs GH¢ 950.00 to produce 600 bricks and GH¢ 1,030.00 to produce 1000 bricks, (i) find the relationship between c, h and n; (ii) calculate the cost of producing 500 bricks.
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(a)(i) Universal set = students in the school; circle L (good Literature students) drawn wholly inside circle G (General Arts class).
(ii) I: not valid (Vivian may be in G but outside L). II: not valid (Audu may be in G but outside L). III: valid (outside G means outside L).
(b)(i) c = h + kn
950 = h + 600k and 1030 = h + 1000k → 400k = 80 → k = 0.2, h = 830
c = 830 + 0.2n (i.e. c = h + n/5 with h = 830)
(ii) c = 830 + 0.2 × 500 = GH¢ 930.00
A conclusion is valid only if it must be true in the diagram.