MATH213 HW 1
Due Wednesday, August 31
Solve five of the six problems below.
1. For each of the following sets, determine whether 3 is an element of that set and also
whether {3}is an element of that set.
(a) {4,3,{4},3},
(b) {4,{3},{4},{{3}}},
(c) {4,{3,4},{4},{3,{3}}},
(d) {4,{3,3},{4},3,{{3}}},
(e) {4,{{3}},{4},{{3}}}.
Please, explain your answers.
2. Determine whether each of the statements below is true or false.
(a) 0 โ {โ
}; (b) {โ
} =โ
; (c) โ
โ {0}; (d) {โ
,โ
} โ {โ
}; (e) {{โ
}} โ {โ
,{โ
}};
(f) {{โ
}} โ {โ
,{โ
}}.
3. Let A={x},B={1,2,3}, and C={b, c}. Find
(a) BรC; (b) AรCรB; (c) CรBรC.
4. Translate each of the quantifications below into English and determine its truth value:
(a) โyโR(y+ 2 > y)
(b) โxโZโyโR(xโ1> y)
(c) โyโRโxโZ(xโ1> y)
(d) โyโRโxโZ(x2> y)
5. Let A, B, and Cbe sets. Show (in two ways: with the help of membership tables and
by arguing like in Examples 10 and 12) that
(a) AโBโC=AโชBโชC
(b) (AโB)โช(BโA) = (AโชB)โ(AโฉB).
Draw the Wenn diagrams of the righthand sides of (a) and (b).
6. Let A={2,4,6,8,10,11},B={1,2,4,8,9}, and C={1,3,6,8,9,11}. Find
(a) AโฉBโฉC; (b) (AโชB)โC; (c) (AโฉB)โชC.
In each case write the corresponding bit string of length 11.