1.Are |⌊x⌋| and ⌊|x|⌋ always equal? Explain. 2. Are 1 + ⌊x⌋ and ⌊1 + x⌋ always equal? Explain. 3. Are ⌊x⌋ + ⌊y⌋ and ⌊x + y⌋ always equal? Explain. 4. Let x be a real number. Describe (in English) what...

1.Are |⌊x⌋| and ⌊|x|⌋ always equal? Explain.

2. Are 1 + ⌊x⌋ and ⌊1 + x⌋ always equal? Explain.

3. Are ⌊x⌋ + ⌊y⌋ and ⌊x + y⌋ always equal? Explain.

4. Let x be a real number. Describe (in English) what 1 + ⌊x⌋ − ⌈x⌉ represents.

Explain.