Question

对命题p:A∩φ=φ,命题q:A∪φ=A,下列说法正确的是 ()

A．p且q为真 B．p或q为假 C．非p为真 D．非q为真

我需要解释

Answer 1

命题p:A∩φ=φ,任何集合与空集的交集是空集，故p为真，非p为假，C错
命题q:A∪φ=A,,任何集合与空集的并集是该集集故q为真，非q为假，D错
p且q为真 ，选A
p或q为真，B错

Answer 2

A．p且q为真

追问

解释

追答

for x belongs φ
=> x belongs to A and x belongs to φ ( φ is subset of A )
=> x belongs to A∩φ
=>φ is subset of A∩φ
A∩φ is subset of φ

then A∩φ = φ

for x belongs A∪φ
=> x belongs A or x belongs φ
=> x belongs A
=> A∪φ is subset A
for x belongs A
=> x belongs A or x belongs φ
=> x belongs AUφ
=> A is subset A∪φ
then A∪φ = A