# hw4 - EECS 203 HW 4 due Feb 1 2.1 6[E Determine whether{2...

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EECS 203 HW 4 due Feb. 1 2.1 6 [E] Determine whether { 2 } is an element of the following sets. a) { x R | x is an integer greater than 1 } . b) { x R | x is the square of an integer } . c) { 2 , { 2 }} . d) {{ 2 } , {{ 2 }}} . e) {{ 2 } , { 2 , { 2 }}} . f) {{{ 2 }}} . 8 [E] Determine whether each of these statements is true or false. a) ∅ ∈ {∅} . b) ∅ ∈ {∅ , {∅}} . c) {∅} ∈ {∅} . d) {∅} ∈ {{∅}} . e) {∅} ⊂ {∅ , {∅}} . f) {{∅}} ⊂ {∅ , {∅}} . g) {{∅}} ⊂ {{∅} , {∅}} . 22 [M] Determine whether each of these sets is the power set of a set, where a and b are distinct elements. a) b) {∅ , { a }} c) {∅ , { a } , {∅ , a }} d) {∅ , { a } , { b } , { a, b }} 28 [M] Let A = { a, b, c } , B = { x, y } , and C = { 0 , 1 } . Find a) A × B × C b) C × B × A c) C × A × B d) B × B × B 2.2 2 [E] Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B .

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a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at your school who are not taking discrete mathemat- ics c)
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